appendix to the report on the simulation results · 2013. 8. 18. · evaluation oliver bode,...

Advanced Methodology for European Laeken Indicators

Deliverable 7.1 Appendix

Appendix to the Report on theSimulation Results

Version: Final Version - 2011

Andreas Alfons, Christian Bruch, Peter Filzmoser, Monique Graf,

Beat Hulliger, Jan-Philipp Kolb, Risto Lehtonen, Daniela

Lussmann, Angelika Meraner, Ralf Münnich, Desislava

Nedyalkova, Tobias Schoch, Matthias Templ, Maria Valaste, Ari

Veijanen, Stefan Zins

The project FP7–SSH–2007–217322 AMELI is supported by European Commissionfunding from the Seventh Framework Programme for Research.

http://ameli.surveystatistics.net/


II

Main ResponsibilityBeat Hulliger (Workpackage leader)University of Applied Sciences Northwestern SwitzerlandSchool of BusinessRiggenbachstrasse 16, 4600 Olten SwitzerlandE-Mail: [email protected]: +41 62 2860158

List of ContributorsChristian Bruch, Jan-Philipp Kolb, Ralf Münnich, and Stefan ZinsUniversity of Trier

Beat Hulliger, Daniela Lussmann, and Tobias SchochUniversity of Applied Sciences Northwestern Switzerland

Monique Graf and Desislava NedyalkovaSwiss Federal Statistical Office

Risto Lehtonen, Ari Veijanen, and Maria ValasteUniversity of Helsinki

Andreas Alfons, Peter Filzmoser, Angelika Meraner and Matthias TemplTechnical University Vienna

EvaluationOliver Bode, Federal Statistical Office of GermanyThomas Burg, Statistics AustriaRudi Seljak, Statistical Office of the Republic of Slovenia

© http://ameli.surveystatistics.net/ - Final Version - 2011


Contents

A. Overview simulation results (metalist) 3

B. Appendix SFSO 11B.1. Simulation metadata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11B.2. Estimator Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

B.2.1. Parametric estimation of the parameters of the GB2 distributionand the median, ARPR, RMPG, QSR, GINI @ AMELIA . . . . . . 15

B.2.2. Point estimates of the fitted GB2 parameters, simulation type 1 ofTable B.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

B.2.3. Variance estimates of the fitted GB2 parameters, simulation type 1of Table B.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

B.2.4. Point estimates of the fitted GB2 indicators, simulation type 1 ofTable B.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

B.2.5. Variance estimates of the fitted GB2 indicators, simulation type 1of Table B.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

B.2.6. Point estimates of the fitted GB2 parameters, simulation type 2 ofTable B.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

B.2.7. Variance estimates of the fitted GB2 parameters, simulation type 2of Table B.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

B.2.8. Point estimates of the fitted GB2 indicators, simulation type 2 ofTable B.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

B.2.9. Variance estimates of the fitted GB2 indicators, simulation type 2of Table B.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

C. Appendix UH: Estimation for domains and small areas for AMELIApopulation 55C.1. Simulation Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55C.2. This Document . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55C.3. Estimator Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55C.4. Results for poverty rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

C.4.1. Poverty rate in Amelia, no weights in model fitting, no ISCED inmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

C.4.2. Poverty rate in Amelia, no weights in model fitting but ISCED inmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

C.4.3. Poverty rate in Amelia, weights in model fitting but no ISCED inmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

C.5. Results for Gini coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . 67C.5.1. Gini coefficient in Amelia . . . . . . . . . . . . . . . . . . . . . . . 67

C.6. Results for QSR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71C.6.1. QSR in Amelia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

AMELI-WP7-D7.1-Appendix

IV Contents

D. Appendix UT 75

D.1. AMELI Simulation: ARPR, RMPG, QSR, GINI and MEAN @ AMELIAfor Design 1.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

D.1.1. Estimator Specifications . . . . . . . . . . . . . . . . . . . . . . . . 75

D.1.2. Sampling Designs, Statistics and Variance Estimation Methods . . . 75

D.1.3. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

D.1.4. Point Estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

D.1.5. Direct Variance Estimation Methods . . . . . . . . . . . . . . . . . 76

D.1.6. Comments, Notation and Specifications . . . . . . . . . . . . . . . . 79

D.1.7. Nomenclatura . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

D.2. AMELI Simulation: ARPR, RMPG, QSR, GINI and MEAN @ AMELIAfor Design 1.4a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79



D.2.3. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79




D.2.7. Nomenclatura . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

D.3. AMELI Simulation: ARPR, RMPG, QSR, GINI and MEAN @ AMELIAfor Design 1.5a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85



D.3.3. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86




D.3.7. Nomenclatura . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106




D.4.3. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107




D.4.7. Nomenclatura . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127




D.5.3. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127




D.5.7. Nomenclatura . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133



Contents V

E. Appendix FHNW 135E.1. Synthesis of QSR estimators for AMELIA with simple random sampling . 135

E.1.1. Simulation Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135E.1.2. This Document . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135E.1.3. Estimator Specifications . . . . . . . . . . . . . . . . . . . . . . . . 135E.1.4. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135E.1.5. Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143E.1.6. Comments, Notation and Specifications . . . . . . . . . . . . . . . . 148E.1.7. Nomenclatura . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

E.2. Preliminaries for AMELIA universe . . . . . . . . . . . . . . . . . . . . . . 149E.2.1. Comments, Notation and Specifications . . . . . . . . . . . . . . . . 149E.2.2. Nomenclatura . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

E.3. N0012: SQSR @ AMELIA: sthhsrs1kx6k . . . . . . . . . . . . . . . . . . . 149E.3.1. Simulation Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150E.3.2. Estimator Specifications . . . . . . . . . . . . . . . . . . . . . . . . 150E.3.3. Robustness Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 150E.3.4. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151E.3.5. Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

E.4. N0011: TQSR @ AMELIA: hhsrs1kx6k . . . . . . . . . . . . . . . . . . . . 160E.4.1. Simulation Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160E.4.2. Estimator Specifications . . . . . . . . . . . . . . . . . . . . . . . . 160E.4.3. Robustness Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 160E.4.4. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161E.4.5. Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

E.5. N0012: SQSR @ AMELIA: sthhsrs1kx6k . . . . . . . . . . . . . . . . . . . 170E.5.1. Simulation Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170E.5.2. Estimator Specifications . . . . . . . . . . . . . . . . . . . . . . . . 170E.5.3. Robustness Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 170E.5.4. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171E.5.5. Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

E.6. N0009: TQSR @ AMELIA: sthhsrs1kx6k . . . . . . . . . . . . . . . . . . . 180E.6.1. Simulation Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180E.6.2. Estimator Specifications . . . . . . . . . . . . . . . . . . . . . . . . 180E.6.3. Robustness Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 180E.6.4. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181E.6.5. Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

E.7. N0014: SQSR @ AMELIA: sthhpps1kx6k . . . . . . . . . . . . . . . . . . . 190E.7.1. Simulation Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190E.7.2. Estimator Specifications . . . . . . . . . . . . . . . . . . . . . . . . 190E.7.3. Robustness Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 190E.7.4. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191E.7.5. Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195

E.8. N0015: TQSR @ AMELIA: sthhpps1kx6k . . . . . . . . . . . . . . . . . . 197E.8.1. Simulation Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197E.8.2. Estimator Specifications . . . . . . . . . . . . . . . . . . . . . . . . 197E.8.3. Robustness Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 197E.8.4. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198


VI Contents

E.8.5. Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202

E.9. Preliminaries for AAT-SILC universe . . . . . . . . . . . . . . . . . . . . . 205

E.9.1. Comments, Notation and Specifications . . . . . . . . . . . . . . . . 205

E.9.2. Nomenclatura . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205

E.10.N0001-a): RHT @ A-ATSILC: hhsrs1kx6k . . . . . . . . . . . . . . . . . . 205

E.10.1. Simulation Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206

E.10.2. Estimator Specifications . . . . . . . . . . . . . . . . . . . . . . . . 206

E.10.3. Robustness Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 206

E.10.4. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207

E.10.5. Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

E.11.N0001-b): TM @ A-ATSILC: hhsrs1kx6k . . . . . . . . . . . . . . . . . . . 214




E.11.4. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215

E.11.5. Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220

E.12.N0002: BQSR @ A-ATSILC: hhsrs1kx6k . . . . . . . . . . . . . . . . . . . 225




E.12.4. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226

E.12.5. Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230

E.13.N0003: SQSR @ A-ATSILC: hhsrs1kx6k . . . . . . . . . . . . . . . . . . . 232




E.13.4. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233

E.13.5. Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237

E.14.N0004: TQSR @ A-ATSILC: hhsrs1kx6k . . . . . . . . . . . . . . . . . . . 240




E.14.4. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241

E.14.5. Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244

E.15.N0005: RHT @ A-ATSILC: sthhsrs1kx6k . . . . . . . . . . . . . . . . . . . 246




E.15.4. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247

E.15.5. Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250

E.16.N0008: SQSR @ A-ATSILC: sthhsrs1kx6k . . . . . . . . . . . . . . . . . . 255




E.16.4. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256

E.16.5. Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259



Contents 1

E.17.N0009: TQSR @ A-ATSILC: sthhsrs1kx6k . . . . . . . . . . . . . . . . . . 264E.17.1. Simulation Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264E.17.2. Estimator Specifications . . . . . . . . . . . . . . . . . . . . . . . . 264E.17.3. Robustness Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 264E.17.4. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265E.17.5. Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268

F. Appendix TUW 273F.1. Description of methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273F.2. Social inclusion indicators . . . . . . . . . . . . . . . . . . . . . . . . . . . 273

F.2.1. Quintile share ratio (QSR) . . . . . . . . . . . . . . . . . . . . . . . 273F.2.2. Gini coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273

F.3. Pareto tail modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273F.3.1. Estimation of the shape parameter . . . . . . . . . . . . . . . . . . 275

F.4. Parametric estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276F.5. Simulation results: AAT-SILC . . . . . . . . . . . . . . . . . . . . . . . . . 276

F.5.1. Quintile share ratio (QSR) . . . . . . . . . . . . . . . . . . . . . . . 276F.5.2. Gini coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379F.5.3. Mean equivalized disposable income . . . . . . . . . . . . . . . . . . 481

F.6. Simulation results: AMELIA . . . . . . . . . . . . . . . . . . . . . . . . . . 581F.6.1. Quintile share ratio (QSR) . . . . . . . . . . . . . . . . . . . . . . . 582F.6.2. Gini coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674F.6.3. Mean equivalized disposable income . . . . . . . . . . . . . . . . . . 764

F.7. Discussion and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 852

G. Specific R-Code for simulations 857G.1. Additional R Code for Missingness . . . . . . . . . . . . . . . . . . . . . . . 857G.2. R-Code for Contamination . . . . . . . . . . . . . . . . . . . . . . . . . . . 858

G.2.1. Standard Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 858G.2.2. Alternative Functions . . . . . . . . . . . . . . . . . . . . . . . . . . 861

G.3. R Functions for Computing Point and Variance Estimates . . . . . . . . . 864G.3.1. C Subroutines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 869

*


Appendix A.

Overview simulation results(metalist)

The simulations run by the AMELI project are synthesised in the following Tables. Therehave been many simulations of the AMELI project outside this scheme to develop methodsor investigate particular aspects. The simulations in Tables A.1, A.2 and A.3 are the finalofficial runs.

Table A.1.: Metalist of the simulation runs of the AMELI-project, part 1

id author date mean arpr rmpg qsr gini other universe domain

N0001 FHNW 20101211 1 0 0 0 0 0 AAT-SILC 0N0002 FHNW 20101227 0 0 0 1 0 0 AAT-SILC 0N0003 FHNW 20101228 0 0 0 1 0 0 AAT-SILC 0N0004 FHNW 20101223 0 0 0 1 0 0 AAT-SILC 0N0005 FHNW 20101130 1 0 0 0 0 0 AAT-SILC 0N0006 FHNW 20101201 1 0 0 0 0 0 AAT-SILC 0N0007 FHNW 20101228 0 0 0 1 0 0 AAT-SILC 0N0008 FHNW 20101229 0 0 0 1 0 0 AAT-SILC 0N0009 FHNW 20101224 0 0 0 1 0 0 AAT-SILC 0N0010 FHNW 20101230 0 0 0 1 0 0 AMELIA 0N0011 FHNW 20101230 0 0 0 1 0 0 AMELIA 0N0012 FHNW 20110111 0 0 0 1 0 0 AMELIA 0N0013 FHNW 20101231 0 0 0 1 0 0 AMELIA 0N0014 FHNW 20110107 0 0 0 1 0 0 AMELIA 0N0015 FHNW 20110106 0 0 0 1 0 0 AMELIA 0T1010 UT 20101102 1 1 1 1 1 0 AMELIA 0T1011 UT 20101112 1 1 1 1 1 0 AMELIA 0T1012 UT 20101112 1 1 1 1 1 0 AMELIA 0T1013 UT 20101112 1 1 1 1 1 0 AMELIA 0T1014 UT 20101112 1 1 1 1 1 0 AMELIA 0T1015 UT 20101112 1 1 1 1 1 0 AMELIA 0W0001 TUW 20110208 0 0 0 1 0 0 AAT-SILC 0W0002 TUW 20110208 0 0 0 1 0 0 AAT-SILC 0W0003 TUW 20110208 0 0 0 1 0 0 AAT-SILC 0W0004 TUW 20110208 0 0 0 0 1 0 AAT-SILC 0W0005 TUW 20110208 0 0 0 0 1 0 AAT-SILC 0W0006 TUW 20110208 0 0 0 0 1 0 AAT-SILC 0W0007 TUW 20110208 1 0 0 0 0 0 AAT-SILC 0W0008 TUW 20110208 1 0 0 0 0 0 AAT-SILC 0W0009 TUW 20110208 1 0 0 0 0 0 AAT-SILC 0T1020 UT 20110409 1 1 1 1 1 0 AMELIA 0T1021 UT 20110409 1 1 1 1 1 0 AMELIA 0T1022 UT 20110409 1 1 1 1 1 0 AMELIA 0


4 Appendix A. Overview simulation results (metalist)


id author date mean arpr rmpg qsr gini other universe domain

T1023 UT 20110409 1 1 1 1 1 0 AMELIA 0T1024 UT 20110409 1 1 1 1 1 0 AMELIA 0S0001 SFSO 20110314 1 1 1 1 1 1 AMELIA 0S0002 SFSO 20110314 1 1 1 1 1 1 AMELIA 0S0003 SFSO 20110314 1 1 1 1 1 1 AMELIA 0S0004 SFSO 20110314 1 1 1 1 1 1 AMELIA 0S0005 SFSO 20110314 1 1 1 1 1 1 AMELIA 0S0006 SFSO 20110407 1 1 1 1 1 1 AMELIA 0S0007 SFSO 20110407 1 1 1 1 1 1 AMELIA 0S0008 SFSO 20110407 1 1 1 1 1 1 AMELIA 0S0009 SFSO 20110407 1 1 1 1 1 1 AMELIA 0S0010 SFSO 20110407 1 1 1 1 1 1 AMELIA 0S0011 SFSO 20110204 1 1 1 1 1 1 AMELIA 0S0012 SFSO 20110204 1 1 1 1 1 1 AMELIA 0S0013 SFSO 20110204 1 1 1 1 1 1 AMELIA 0S0014 SFSO 20110204 1 1 1 1 1 1 AMELIA 0S0015 SFSO 20110204 1 1 1 1 1 1 AMELIA 0S0016 SFSO 20110207 1 1 1 1 1 1 AMELIA 0S0017 SFSO 20110207 1 1 1 1 1 1 AMELIA 0S0018 SFSO 20110207 1 1 1 1 1 1 AMELIA 0S0019 SFSO 20110207 1 1 1 1 1 1 AMELIA 0S0020 SFSO 20110207 1 1 1 1 1 1 AMELIA 0


id design size oc ocpar nr nrpar

N0001 1.2 6000 OCAR-CCAR, OCAR-NCAR, OAR-CCAR, OAR-NCAR

0.01; 0.001 0 0


0.001; 0.01 0 0

N0003 1.2 6000 OAR-NCAR 0.001; 0.01 0 0N0004 1.2 6000 OCAR-CCAR, OCAR-NCAR, OAR-

CCAR, OAR-NCAR0.001; 0.01 0 0

N0005 1.4a 6000 OCAR-CCAR, OCAR-NCAR, OAR-CCAR, OAR-NCAR

0.01; 0.001 0 0

N0006 1.4a 6000 OCAR-NCAR, OCAR-CCAR 0.01; 0.001 0 0N0007 1.4a 6000 OCAR-CCAR, OCAR-NCAR, OAR-

CCAR, OAR-NCAR0.001; 0.01 0 0


0.001; 0.01 0 0


0.01; 0.001 0 0


0.001; 0.01 0 0


0.001; 0.01 0 0


0.001; 0.01 0 0


0.001; 0.01 0 0



5




0.001; 0.01 0 0


0.001; 0.01 0 0

T1010 all 6000 0 0 0 0T1011 1.2a 6000 OCAR.NCAR [OCAR|

NA| CCAR|rnorm(5e+05||20000)and OCAR| NA|NCAR| (12) and0.01| OCAR|NA| NCAR|(12) and OAR|RB210| 0.7| 0.1|0.15| 0.05| CCAR|rnorm(5e+05||20000)and OAR| RB210|0.7| 0.1| 0.15| 0.05|NCAR| (12) ] X[0.001 OEps and0.01 OEps]

0 0

T1012 1.4a 6000 OCAR.NCAR [OCAR|NA| CCAR|rnorm(5e+05||20000)and OCAR| NA|NCAR| (12) and0.01| OCAR|NA| NCAR|(12) and OAR|RB210| 0.7| 0.1|0.15| 0.05| CCAR|rnorm(5e+05||20000)and OAR| RB210|0.7| 0.1| 0.15| 0.05|NCAR| (12) ] X[0.001 OEps and0.01 OEps]

0 0

T1013 1.5a 6000 OCAR.NCAR [OCAR|NA| CCAR|rnorm(5e+05||20000)and OCAR| NA|NCAR| (12) and0.01| OCAR|NA| NCAR|(12) and OAR|RB210| 0.7| 0.1|0.15| 0.05| CCAR|rnorm(5e+05||20000)and OAR| RB210|0.7| 0.1| 0.15| 0.05|NCAR| (12) ] X[0.001 OEps and0.01 OEps]

0 0





T1014 2.6 6000 OCAR.NCAR [OCAR|NA| CCAR|rnorm(5e+05||20000)and OCAR| NA|NCAR| (12) and0.01| OCAR|NA| NCAR|(12) and OAR|RB210| 0.7| 0.1|0.15| 0.05| CCAR|rnorm(5e+05||20000)and OAR| RB210|0.7| 0.1| 0.15| 0.05|NCAR| (12) ] X[0.001 OEps and0.01 OEps]

0 0

T1015 2.7 6000 OCAR.NCAR [OCAR|NA| CCAR|rnorm(5e+05||20000)and OCAR| NA|NCAR| (12) and0.01| OCAR|NA| NCAR|(12) and OAR|RB210| 0.7| 0.1|0.15| 0.05| CCAR|rnorm(5e+05||20000)and OAR| RB210|0.7| 0.1| 0.15| 0.05|NCAR| (12) ] X[0.001 OEps and0.01 OEps]

0 0

W0001 1.2 6000 OCAR-CCAR, OCAR-NCAR, OAR-CCAR, OAR-NCAR

epsilon=0.01 andepsilon=0.001;mu=300000 andmu=500000

0 0

W0002 1.4a 6000 OCAR-CCAR, OCAR-NCAR, OAR-CCAR, OAR-NCAR


0 0



0 0



0 0



0 0



7





0 0



0 0



0 0



0 0

T1020 1.2 6000 NA NA NA NAT1021 1.4a 6000 NA NA NA NAT1022 1.5a 6000 NA NA NA NAT1023 2.6 6000 NA NA NA NAT1024 2.7 6000 NA NA NA NAS0001 1.2 6000 NA NA NA NAS0002 1.4a 6000 NA NA NA NAS0003 1.5a 6004 NA NA NA NAS0004 2.6 6000 NA NA NA NAS0005 2.7 6000 NA NA NA NAS0006 1.2 6000 NA NA NA NAS0007 1.4a 6000 NA NA NA NAS0008 1.5a 6004 NA NA NA NAS0009 2.6 6000 NA NA NA NAS0010 2.7 6000 NA NA NA NAS0011 1.2 6000 NA NA NA NAS0012 1.4a 6000 NA NA NA NAS0013 1.5a 6004 NA NA NA NAS0014 2.6 6000 NA NA NA NAS0015 2.7 6000 NA NA NA NAS0016 1.2 6000 NA NA NA NAS0017 1.4a 6000 NA NA NA NAS0018 1.5a 6004 NA NA NA NAS0019 2.6 6000 NA NA NA NAS0020 2.7 6000 NA NA NA NANote: designs=all: 1.2, 1.4a, 1.5a. 2.6, 2.7. indicator: m=mean, a= arpr, r= rmpg, q=qsr,g=gini, o=other. *: [OCAR| NA| CCAR| rnorm(5e+05||20000) and OCAR| NA| NCAR|(12) and 0.01| OCAR| NA| NCAR| (12) and OAR| RB210| 0.7| 0.1| 0.15| 0.05| CCAR|rnorm(5e+05||20000) and OAR| RB210| 0.7| 0.1| 0.15| 0.05| NCAR| (12) ] X [0.001 OEpsand 0.01 OEps]




id nrep sw

N0001 1000 DbsimN0002 1000 DbsimN0003 1000 DbsimN0004 1000 DbsimN0005 1000 DbsimN0006 1000 DbsimN0007 1000 DbsimN0008 1000 DbsimN0009 1000 DbsimN0010 1000 DbsimN0011 1000 DbsimN0012 1000 DbsimN0013 1000 DbsimN0014 1000 DbsimN0015 1000 DbsimT1010 10000 condorT1011 10000 condorT1012 10000 condorT1013 10000 condorT1014 10000 condorT1015 10000 condorW0001 1000 simFrameW0002 1000 simFrameW0003 1000 simFrameW0004 1000 simFrameW0005 1000 simFrameW0006 1000 simFrameW0007 1000 simFrameW0008 1000 simFrameW0009 1000 simFrameT1020 10000 condorT1021 10000 condorT1022 10000 condorT1023 10000 condorT1024 10000 condorS0001 1000 condorS0002 1000 condorS0003 1000 condorS0004 1000 condorS0005 1000 condorS0006 1000 condorS0007 1000 condorS0008 1000 condorS0009 1000 condorS0010 1000 condorS0011 1000 condorS0012 1000 condorS0013 1000 condorS0014 1000 condorS0015 1000 condorS0016 1000 condorS0017 1000 condor



9


id nrep sw

S0018 1000 condorS0019 1000 condorS0020 1000 condor


Appendix B.

Appendix SFSO

B.1. Simulation metadata

Table B.1.: Simulation using the profile log-likelihood, robustified weights, AMELIA re-gional level

ID S0001 S0002 S0003 S0004 S0005Author SFSODate 20110314Median 1 1 1 1 1ARPR 1 1 1 1 1RMPG 1 1 1 1 1QSR 1 1 1 1 1Gini 1 1 1 1 1a 1 1 1 1 1b 1 1 1 1 1p 1 1 1 1 1q 1 1 1 1 1Domains: [none] (default)Universe: AMELIASample design d1.2 d1.4a d1.5a d2.6 d2.7Sample Size 6000 6000 6004 6000 6000MonteCarlo Replicates: 1,000 (default)Criteria Set: Univariate criteria (default)Outlyingness: [none] (default)Contamination: [none] (default)Missingness: [none] (default)Simulation Environment: Condor

B.2. Estimator Specifications

Pseudo maximum likelihood estimators, based on the maximum log-likelihood, ofthe GB2 parameters a, b, p and q,

Pseudo maximum likelihood estimators, based on the maximum log-likelihood, ofthe median, the ARPR, the RMPG, the QSR and the Gini index,


12 Appendix B. Appendix SFSO

Table B.2.: Simulation using the profile log-likelihood, robustified weights, AMELIAglobal level




B.2. Estimator Specifications 13

Table B.3.: Simulation using the full log-likelihood, robustified weights, AMELIA globallevel




Table B.4.: Simulation using the full log-likelihood, non-robustified weights, AMELIAglobal level





Variance estimators of the fitted GB2 parameters and indicators based on lineariza-tion.

B.2.1. Parametric estimation of the parameters of the GB2distribution and the median, ARPR, RMPG, QSR, GINI@ AMELIA

In this section, we summarize the performance of the estimators due to different crite-ria. The general univariate measures of comparison are described in details in Chapter2. Additional measures will be described. The different simulation types are given inTable B.5.

Table B.5.: Summary of the different simulations

Method of estimation Sampling weights AMELIA levelOriginal Robust Global Regional

1 ML full + + + -2 ML prof - + + +3 NLS + - + +4 Compound - + - +

B.2.2. Point estimates of the fitted GB2 parameters, simulationtype 1 of Table B.5

In Tables B.6, B.7, B.8 and B.9 we can see the following specific notation:

T: point estimator of the fitted GB2 parameter (a, b, p, q),

adj: if the weights were robustified (yes) or not (no),

design: the used sampling design for the sample drawn from the AMELIA universe,

cvsT: coefficient of variation of the fitted parameter over the 1000 simulations,

cvT: mean over all simulations of the coefficient of variation, calculated using the varianceestimator by linearization,

cvdT: mean over all simulations of the coefficient of variation, calculated using the vari-ance estimator by linearization and the full design information.

Note that for design d2.6, we were not able to calculate variance estiamtors using thewhole design information, thus the values in the tables are equal to 0.



Tab

leB

.6.:P

oint

estimator

ofa

Tad

jdesign

avgT

mad

TvarT

cvsT

cvT

cvdT

ano

d1.2

4.391e+00

4.027e-011.797e-01

9.654e-029.343e-02

9.343e-02a

yesd1.2

3.833e+00

3.240e-011.203e-01

9.051e-029.380e-02

9.380e-02a

no

d1.4a

4.415e+00

3.995e-011.800e-01

9.608e-029.813e-02

9.790e-02a

yesd1.4a

3.854e+00

3.290e-011.211e-01

9.029e-029.160e-02

9.134e-02a

no

d1.5a

4.376e+00

3.930e-011.630e-01

9.227e-028.327e-02

8.295e-02a

yesd1.5a

3.835e+00

3.307e-011.177e-01

8.947e-028.294e-02

8.258e-02a

no

d2.6

4.415e+00

4.800e-012.114e-01

1.041e-018.248e-02

0.000e+00

ayes

d2.6

3.865e+00

3.887e-011.538e-01

1.015e-018.437e-02

0.000e+00

ano

d2.7

4.424e+00

4.783e-012.438e-01

1.116e-018.939e-02

1.009e-01a

yesd2.7

3.866e+00

4.095e-011.676e-01

1.059e-019.006e-02

1.035e-01




Tab

leB

.7.:

Poi

nt

esti

mat

orofb

Tad

jdes

ign

avgT

mad

Tva

rTcv

sTcv

Tcv

dT

bno

d1.

24.

700e

+04

1.91

3e+

036.

410e

+06

5.38

7e-0

24.

887e

-02

4.88

7e-0

2b

yes

d1.

24.

721e

+04

2.21

3e+

036.

962e

+06

5.58

9e-0

25.

405e

-02

5.40

5e-0

2b

no

d1.

4a4.

683e

+04

2.06

7e+

035.

770e

+06

5.13

0e-0

25.

188e

-02

5.16

6e-0

2b

yes

d1.

4a4.

706e

+04

2.28

9e+

036.

253e

+06

5.31

4e-0

25.

252e

-02

5.23

2e-0

2b

no

d1.

5a4.

700e

+04

1.86

8e+

035.

346e

+06

4.91

9e-0

24.

329e

-02

4.29

9e-0

2b

yes

d1.

5a4.

716e

+04

2.20

0e+

036.

127e

+06

5.24

8e-0

24.

816e

-02

4.78

8e-0

2b

no

d2.

64.

688e

+04

2.05

9e+

035.

355e

+06

4.93

6e-0

24.

220e

-02

0.00

0e+

00b

yes

d2.

64.

715e

+04

2.32

0e+

036.

271e

+06

5.31

1e-0

24.

871e

-02

0.00

0e+

00b

no

d2.

74.

680e

+04

2.14

1e+

036.

027e

+06

5.24

6e-0

24.

583e

-02

4.82

8e-0

2b

yes

d2.

74.

707e

+04

2.49

2e+

036.

704e

+06

5.50

1e-0

25.

179e

-02

5.32

7e-0

2



Tab

leB

.8.:P

oint

estimator

ofp

Tad

jdesign

avgT

mad

TvarT

cvsT

cvT

cvdT

pno

d1.2

2.568e-012.665e-02

7.391e-041.058e-01

1.031e-011.031e-01

pyes

d1.2

3.212e-013.220e-02

1.125e-031.044e-01

1.045e-011.045e-01

pno

d1.4a

2.556e-012.716e-02

7.255e-041.054e-01

1.081e-011.080e-01

pyes

d1.4a

3.194e-013.139e-02

1.090e-031.034e-01

1.020e-011.018e-01

pno

d1.5a

2.577e-012.723e-02

7.411e-041.056e-01

9.487e-029.465e-02

pyes

d1.5a

3.211e-013.275e-02

1.160e-031.061e-01

9.410e-029.383e-02

pno

d2.6

2.564e-012.881e-02

7.692e-041.082e-01

9.404e-020.000e+

00p

yesd2.6

3.201e-013.456e-02

1.228e-031.095e-01

9.569e-020.000e+

00p

no

d2.7

2.564e-012.960e-02

8.990e-041.170e-01

9.868e-021.053e-01

pyes

d2.7

3.208e-013.615e-02

1.322e-031.133e-01

1.002e-011.094e-01




Tab

leB

.9.:

Poi

nt

esti

mat

orofq

Tad

jdes

ign

avgT

mad

Tva

rTcv

sTcv

Tcv

dT

qno

d1.

21.

014e

+00

1.48

6e-0

13.

643e

-02

1.88

2e-0

11.

657e

-01

1.65

7e-0

1q

yes

d1.

21.

204e

+00

1.76

1e-0

14.

629e

-02

1.78

7e-0

11.

720e

-01

1.72

0e-0

1q

no

d1.

4a1.

002e

+00

1.41

0e-0

13.

324e

-02

1.82

0e-0

11.

754e

-01

1.75

2e-0

1q

yes

d1.

4a1.

190e

+00

1.83

8e-0

14.

275e

-02

1.73

7e-0

11.

675e

-01

1.67

2e-0

1q

no

d1.

5a1.

017e

+00

1.46

8e-0

13.

253e

-02

1.77

4e-0

11.

484e

-01

1.48

0e-0

1q

yes

d1.

5a1.

201e

+00

1.88

9e-0

14.

345e

-02

1.73

6e-0

11.

541e

-01

1.53

6e-0

1q

no

d2.

61.

006e

+00

1.67

2e-0

13.

342e

-02

1.81

8e-0

11.

459e

-01

0.00

0e+

00q

yes

d2.

61.

193e

+00

1.98

1e-0

14.

787e

-02

1.83

4e-0

11.

565e

-01

0.00

0e+

00q

no

d2.

71.

004e

+00

1.62

3e-0

13.

815e

-02

1.94

6e-0

11.

564e

-01

1.64

0e-0

1q

yes

d2.

71.

193e

+00

2.03

7e-0

14.

863e

-02

1.84

9e-0

11.

648e

-01

1.75

1e-0

1



B.2.3. Variance estimates of the fitted GB2 parameters,simulation type 1 of Table B.5


V: variance estimator of the fitted GB2 parameter (a, b, p, q),

def: if the variance is calculated using the whole design information (2) or not (1),

adj: if the weights were robustified (yes) or not (no),

design: the used sampling design for the sample drawn from the AMELIA universe

Table B.10.: Variance estimator of a

V def adj design avgV biasV relbiasV%a 1 no d1.2 1.972e-01 1.744e-02 9.703e+00a 2 no d1.2 1.971e-01 1.740e-02 9.680e+00a 1 yes d1.2 2.039e-01 8.355e-02 6.943e+01a 2 yes d1.2 2.039e-01 8.356e-02 6.944e+01a 1 no d1.4a 3.326e-01 1.526e-01 8.480e+01a 2 no d1.4a 3.313e-01 1.514e-01 8.410e+01a 1 yes d1.4a 1.328e-01 1.168e-02 9.651e+00a 2 yes d1.4a 1.320e-01 1.096e-02 9.049e+00a 1 no d1.5a 1.528e-01 -1.017e-02 -6.241e+00a 2 no d1.5a 1.517e-01 -1.134e-02 -6.954e+00a 1 yes d1.5a 1.078e-01 -9.880e-03 -8.391e+00a 2 yes d1.5a 1.069e-01 -1.083e-02 -9.197e+00a 1 no d2.6 1.462e-01 -6.517e-02 -3.082e+01a 1 yes d2.6 1.345e-01 -1.933e-02 -1.257e+01a 1 no d2.7 1.707e-01 -7.311e-02 -2.998e+01a 2 no d2.7 2.172e-01 -2.661e-02 -1.091e+01a 1 yes d2.7 1.253e-01 -4.230e-02 -2.525e+01a 2 yes d2.7 1.671e-01 -4.200e-04 -2.500e-01




Table B.11.: Variance estimator of b

V def adj design avgV biasV relbiasV%b 1 no d1.2 1.129e+07 4.876e+06 7.606e+01b 2 no d1.2 1.128e+07 4.865e+06 7.590e+01b 1 yes d1.2 9.971e+06 3.009e+06 4.322e+01b 2 yes d1.2 9.972e+06 3.009e+06 4.322e+01b 1 no d1.4a 3.897e+07 3.320e+07 5.754e+02b 2 no d1.4a 3.881e+07 3.304e+07 5.727e+02b 1 yes d1.4a 7.251e+06 9.978e+05 1.596e+01b 2 yes d1.4a 7.200e+06 9.471e+05 1.515e+01b 1 no d1.5a 8.506e+06 3.159e+06 5.910e+01b 2 no d1.5a 8.419e+06 3.072e+06 5.747e+01b 1 yes d1.5a 6.018e+06 -1.091e+05 -1.781e+00b 2 yes d1.5a 5.953e+06 -1.743e+05 -2.846e+00b 1 no d2.6 7.664e+06 2.309e+06 4.312e+01b 1 yes d2.6 7.460e+06 1.189e+06 1.896e+01b 1 no d2.7 6.499e+06 4.723e+05 7.836e+00b 2 no d2.7 7.073e+06 1.046e+06 1.736e+01b 1 yes d2.7 6.625e+06 -7.867e+04 -1.173e+00b 2 yes d2.7 6.971e+06 2.666e+05 3.976e+00

Table B.12.: Variance estimator of p

V def adj design avgV biasV relbiasV%p 1 no d1.2 1.00e-03 2.70e-04 3.591e+01p 2 no d1.2 1.00e-03 2.60e-04 3.585e+01p 1 yes d1.2 1.80e-03 6.70e-04 5.981e+01p 2 yes d1.2 1.80e-03 6.70e-04 5.982e+01p 1 no d1.4a 2.17e-03 1.44e-03 1.992e+02p 2 no d1.4a 2.16e-03 1.44e-03 1.983e+02p 1 yes d1.4a 1.18e-03 9.00e-05 7.803e+00p 2 yes d1.4a 1.17e-03 8.00e-05 7.456e+00p 1 no d1.5a 8.00e-04 6.00e-05 8.369e+00p 2 no d1.5a 8.00e-04 6.00e-05 7.783e+00p 1 yes d1.5a 1.02e-03 -1.40e-04 -1.226e+01p 2 yes d1.5a 1.01e-03 -1.50e-04 -1.278e+01p 1 no d2.6 7.40e-04 -3.00e-05 -3.667e+00p 1 yes d2.6 1.45e-03 2.20e-04 1.784e+01p 1 no d2.7 7.40e-04 -1.60e-04 -1.749e+01p 2 no d2.7 8.70e-04 -3.00e-05 -3.697e+00p 1 yes d2.7 1.08e-03 -2.40e-04 -1.848e+01p 2 yes d2.7 1.35e-03 3.00e-05 1.918e+00



Table B.13.: Variance estimator of q

V def adj design avgV biasV relbiasV%q 1 no d1.2 7.830e-02 4.187e-02 1.149e+02q 2 no d1.2 7.822e-02 4.179e-02 1.147e+02q 1 yes d1.2 7.566e-02 2.937e-02 6.344e+01q 2 yes d1.2 7.567e-02 2.937e-02 6.345e+01q 1 no d1.4a 2.934e-01 2.601e-01 7.827e+02q 2 no d1.4a 2.924e-01 2.592e-01 7.798e+02q 1 yes d1.4a 5.005e-02 7.300e-03 1.708e+01q 2 yes d1.4a 4.989e-02 7.140e-03 1.671e+01q 1 no d1.5a 5.860e-02 2.608e-02 8.017e+01q 2 no d1.5a 5.821e-02 2.568e-02 7.897e+01q 1 yes d1.5a 4.255e-02 -9.000e-04 -2.080e+00q 2 yes d1.5a 4.229e-02 -1.160e-03 -2.674e+00q 1 no d2.6 5.284e-02 1.942e-02 5.811e+01q 1 yes d2.6 5.678e-02 8.910e-03 1.862e+01q 1 no d2.7 4.016e-02 2.020e-03 5.286e+00q 2 no d2.7 4.447e-02 6.320e-03 1.657e+01q 1 yes d2.7 4.493e-02 -3.690e-03 -7.592e+00q 2 yes d2.7 5.209e-02 3.470e-03 7.128e+00




B.2.4. Point estimates of the fitted GB2 indicators, simulationtype 1 of Table B.5

In Tables B.14, B.15, B.16, B.17 and B.18 the used notation is as for the parameters.



Tab

leB

.14.:P

oint

estimator

ofth

em

edian

Tad

jdesign

avgT

mad

TvarT

cvsT

cvT

cvdT

relbiasT

%M

edian

no

d1.2

2.558e+04

3.172e+02

8.315e+04

1.127e-021.179e-02

1.179e-021.103e-01

Med

ianyes

d1.2

2.585e+04

3.169e+02

8.442e+04

1.124e-021.175e-02

1.175e-021.115e+

00eM

edian

no

d1.2

2.557e+04

-1.069e+

051.279e-02

--

-M

edian

no

d1.4a

2.559e+04

2.765e+02

7.426e+04

1.065e-021.192e-02

1.108e-028.527e-02

Med

ianyes

d1.4a

2.586e+04

2.577e+02

7.536e+04

1.062e-021.167e-02

1.083e-021.104e+

00eM

edian

no

d1.4a

2.558e+04

-9.798e+

041.224e-02

--

-M

edian

no

d1.5a

2.556e+04

2.231e+02

5.646e+04

9.290e-031.059e-02

9.650e-037.361e-02

Med

ianyes

d1.5a

2.584e+04

2.269e+02

5.453e+04

9.040e-031.039e-02

9.450e-031.121e+

00eM

edian

no

d1.5a

2.555e+04

-7.156e+

041.047e-02

--

-M

edian

no

d2.6

2.563e+04

7.913e+02

8.638e+05

3.627e-021.057e-02

0.000e+00

7.321e-02M

edian

yesd2.6

2.595e+04

7.246e+02

8.718e+05

3.598e-021.041e-02

0.000e+00

1.103e+00

eMed

ianno

d2.6

2.568e+04

-8.625e+

053.617e-02

--

-M

edian

no

d2.7

2.560e+04

7.463e+02

8.323e+05

3.563e-021.169e-02

3.000e-021.061e-01

Med

ianyes

d2.7

2.594e+04

7.323e+02

8.444e+05

3.543e-021.160e-02

2.897e-021.125e+

00eM

edian

no

d2.7

2.566e+04

-8.579e+

053.610e-02

--

-




Tab

leB

.15.

:P

oint

esti

mat

orof

AR

PR

and

eAR

PR

Tad

jdes

ign

avgT

mad

Tva

rTcv

sTcv

Tcv

dT

relb

iasT

%A

RP

Rno

d1.

22.

872e

+01

2.80

6e-0

17.

547e

-02

9.56

0e-0

39.

630e

-03

9.64

0e-0

38.

739e

+00

AR

PR

yes

d1.

22.

765e

+01

3.00

5e-0

18.

543e

-02

1.05

7e-0

29.

250e

-03

9.25

0e-0

34.

547e

+00

eAR

PR

no

d1.

22.

645e

+01

-2.

763e

-01

1.98

8e-0

2-

--

AR

PR

no

d1.

4a2.

871e

+01

2.66

5e-0

16.

858e

-02

9.12

0e-0

39.

710e

-03

9.65

0e-0

38.

763e

+00

AR

PR

yes

d1.

4a2.

764e

+01

2.77

6e-0

17.

627e

-02

9.99

0e-0

39.

270e

-03

9.20

0e-0

34.

597e

+00

eAR

PR

no

d1.

4a2.

642e

+01

-2.

753e

-01

1.98

6e-0

2-

--

AR

PR

no

d1.

5a2.

873e

+01

2.81

1e-0

18.

601e

-02

1.02

1e-0

21.

022e

-02

1.01

5e-0

28.

817e

+00

AR

PR

yes

d1.

5a2.

765e

+01

2.99

2e-0

18.

950e

-02

1.08

2e-0

29.

280e

-03

9.20

0e-0

34.

643e

+00

eAR

PR

no

d1.

5a2.

642e

+01

-2.

221e

-01

1.78

4e-0

2-

--

AR

PR

no

d2.

62.

868e

+01

3.87

1e-0

11.

671e

-01

1.42

5e-0

21.

028e

-02

-8.

761e

+00

AR

PR

yes

d2.

62.

759e

+01

4.40

1e-0

11.

907e

-01

1.58

3e-0

29.

360e

-03

-4.

676e

+00

eAR

PR

no

d2.

62.

635e

+01

-4.

327e

-01

2.49

6e-0

2-

--

AR

PR

no

d2.

72.

868e

+01

3.81

0e-0

11.

511e

-01

1.35

5e-0

29.

700e

-03

1.22

2e-0

28.

930e

+00

AR

PR

yes

d2.

72.

756e

+01

4.28

2e-0

11.

903e

-01

1.58

2e-0

29.

340e

-03

1.21

2e-0

24.

741e

+00

eAR

PR

no

d2.

72.

631e

+01

-4.

403e

-01

2.52

2e-0

2-

--



Tab

leB

.16.:P

oint

estimator

ofR

MP

G

Tad

jdesign

avgT

mad

TvarT

cvsT

cvT

cvdT

relbiasT

%R

MP

Gno

d1.2

4.667e+01

6.522e-014.027e-01

1.360e-021.368e-02

1.368e-027.016e+

00R

MP

Gyes

d1.2

4.409e+01

7.071e-014.409e-01

1.506e-021.293e-02

1.293e-029.757e-01

eRM

PG

no

d1.2

4.367e+01

-2.038e+

003.269e-02

--

-R

MP

Gno

d1.4a

4.664e+01

6.163e-013.711e-01

1.306e-021.377e-02

1.370e-026.848e+

00R

MP

Gyes

d1.4a

4.407e+01

6.439e-013.970e-01

1.430e-021.290e-02

1.283e-028.677e-01

eRM

PG

no

d1.4a

4.369e+01

-1.992e+

003.230e-02

--

-R

MP

Gno

d1.5a

4.667e+01

6.624e-014.723e-01

1.473e-021.466e-02

1.459e-026.837e+

00R

MP

Gyes

d1.5a

4.408e+01

6.973e-014.749e-01

1.563e-021.313e-02

1.305e-028.692e-01

eRM

PG

no

d1.5a

4.369e+01

-1.784e+

003.057e-02

--

-R

MP

Gno

d2.6

4.658e+01

8.605e-017.811e-01

1.897e-021.473e-02

0.000e+00

7.024e+00

RM

PG

yesd2.6

4.397e+01

8.746e-018.109e-01

2.048e-021.322e-02

0.000e+00

8.531e-01eR

MP

Gno

d2.6

4.356e+01

-2.041e+

003.279e-02

--

-R

MP

Gno

d2.7

4.657e+01

8.163e-017.001e-01

1.797e-021.375e-02

1.639e-026.885e+

00R

MP

Gyes

d2.7

4.392e+01

8.600e-018.038e-01

2.042e-021.295e-02

1.551e-028.430e-01

eRM

PG

no

d2.7

4.354e+01

-2.175e+

003.387e-02

--

-




Tab

leB

.17.

:P

oint

esti

mat

orof

QSR

Tad

jdes

ign

avgT

mad

Tva

rTcv

sTcv

Tcv

dT

relb

iasT

%Q

SR

no

d1.

21.

046e

+01

3.32

5e-0

11.

019e

-01

3.05

1e-0

23.

076e

-02

3.07

6e-0

28.

999e

+00

QSR

yes

d1.

29.

411e

+00

2.98

6e-0

18.

196e

-02

3.04

2e-0

22.

678e

-02

2.67

8e-0

2-2

.155

e+00

eQSR

no

d1.

29.

618e

+00

-9.

037e

-02

3.12

6e-0

2-

--

QSR

no

d1.

4a1.

045e

+01

3.08

6e-0

19.

304e

-02

2.91

8e-0

23.

086e

-02

3.05

8e-0

28.

939e

+00

QSR

yes

d1.

4a9.

402e

+00

2.66

1e-0

17.

059e

-02

2.82

6e-0

22.

677e

-02

2.65

0e-0

2-2

.143

e+00

eQSR

no

d1.

4a9.

605e

+00

-8.

259e

-02

2.99

2e-0

2-

--

QSR

no

d1.

5a1.

047e

+01

3.27

8e-0

11.

119e

-01

3.19

7e-0

23.

208e

-02

3.17

8e-0

28.

940e

+00

QSR

yes

d1.

5a9.

408e

+00

2.91

5e-0

18.

389e

-02

3.07

9e-0

22.

658e

-02

2.62

9e-0

2-2

.172

e+00

eQSR

no

d1.

5a9.

615e

+00

-9.

314e

-02

3.17

4e-0

2-

--

QSR

no

d2.

61.

043e

+01

5.13

7e-0

12.

783e

-01

5.05

9e-0

23.

210e

-02

0.00

0e+

008.

962e

+00

QSR

yes

d2.

69.

357e

+00

4.45

5e-0

12.

186e

-01

4.99

7e-0

22.

664e

-02

0.00

0e+

00-2

.138

e+00

eQSR

no

d2.

69.

553e

+00

-2.

435e

-01

5.16

5e-0

2-

--

QSR

no

d2.

71.

043e

+01

5.09

3e-0

12.

673e

-01

4.95

6e-0

23.

081e

-02

4.28

1e-0

28.

994e

+00

QSR

yes

d2.

79.

336e

+00

4.55

2e-0

12.

232e

-01

5.06

0e-0

22.

673e

-02

3.78

5e-0

2-2

.154

e+00

eQSR

no

d2.

79.

538e

+00

-2.

502e

-01

5.24

4e-0

2-

--



Tab

leB

.18.:P

oint

estimator

ofth

eG

ini

Tad

jdesign

avgT

mad

TvarT

cvsT

cvT

cvdT

relbiasT

%G

ini

no

d1.2

3.844e-014.09e-03

2e-051.045e-02

1.041e-021.041e-02

2.263e+00

Gin

iyes

d1.2

3.751e-014.13e-03

2e-051.094e-02

1.025e-021.025e-02

-2.189e-01eG

ini

no

d1.2

3.759e-01-

2e-051.100e-02

--

-G

ini

no

d1.4a

3.844e-013.75e-03

1e-051.005e-02

1.045e-021.034e-02

2.270e+00

Gin

iyes

d1.4a

3.750e-013.74e-03

1e-051.021e-02

1.027e-021.016e-02

-1.966e-01eG

ini

no

d1.4a

3.757e-01-

2e-051.041e-02

--

-G

ini

no

d1.5a

3.844e-013.94e-03

1e-059.930e-03

1.011e-029.990e-03

2.290e+00

Gin

iyes

d1.5a

3.750e-014.12e-03

1e-051.030e-02

9.640e-039.520e-03

-1.995e-01eG

ini

no

d1.5a

3.758e-01-

2e-051.034e-02

--

-G

i ni

no

d2.6

3.839e-016.85e-03

4e-051.702e-02

1.015e-020.000e+

002.280e+

00G

ini

yesd2.6

3.742e-016.75e-03

5e-051.801e-02

9.680e-030.000e+

00-1.814e-01

eGin

ino

d2.6

3.749e-01-

5e-051.860e-02

--

-G

i ni

no

d2.7

3.840e-016.98e-03

4e-051.732e-02

1.045e-021.506e-02

2.296e+00

Gin

iyes

d2.7

3.740e-016.90e-03

5e-051.866e-02

1.029e-021.487e-02

-1.999e-01eG

ini

no

d2.7

3.748e-01-

5e-051.937e-02

--

-




B.2.5. Variance estimates of the fitted GB2 indicators,simulation type 1 of Table B.5


Table B.19.: Variance estimator of the median

V def adj design avgV biasV relbiasV%Median 1 no d1.2 9.190e+04 8.747e+03 1.052e+01Median 2 no d1.2 9.191e+04 8.758e+03 1.053e+01Median 1 yes d1.2 9.614e+04 1.172e+04 1.389e+01Median 2 yes d1.2 9.616e+04 1.174e+04 1.391e+01Median 1 no d1.4a 9.955e+04 2.529e+04 3.406e+01Median 2 no d1.4a 8.704e+04 1.278e+04 1.721e+01Median 1 yes d1.4a 9.123e+04 1.587e+04 2.106e+01Median 2 yes d1.4a 7.862e+04 3.260e+03 4.326e+00Median 1 no d1.5a 7.390e+04 1.744e+04 3.090e+01Median 2 no d1.5a 6.155e+04 5.094e+03 9.022e+00Median 1 yes d1.5a 7.239e+04 1.786e+04 3.275e+01Median 2 yes d1.5a 5.993e+04 5.401e+03 9.904e+00Median 1 no d2.6 7.355e+04 -7.902e+05 -9.148e+01Median 1 yes d2.6 7.434e+04 -7.975e+05 -9.147e+01Median 1 no d2.7 8.966e+04 -7.427e+05 -8.923e+01Median 2 no d2.7 7.911e+05 -4.127e+04 -4.958e+00Median 1 yes d2.7 9.047e+04 -7.540e+05 -8.929e+01Median 2 yes d2.7 7.687e+05 -7.569e+04 -8.963e+00



Table B.20.: Variance estimator of the ARPR

V def adj design avgV biasV relbiasV%ARPR 1 no d1.2 7.664e-02 1.170e-03 1.546e+00ARPR 2 no d1.2 7.665e-02 1.180e-03 1.562e+00ARPR 1 yes d1.2 6.540e-02 -2.003e-02 -2.344e+01ARPR 2 yes d1.2 6.541e-02 -2.002e-02 -2.343e+01ARPR 1 no d1.4a 7.859e-02 1.001e-02 1.459e+01ARPR 2 no d1.4a 7.760e-02 9.020e-03 1.315e+01ARPR 1 yes d1.4a 6.564e-02 -1.063e-02 -1.393e+01ARPR 2 yes d1.4a 6.460e-02 -1.167e-02 -1.530e+01ARPR 1 no d1.5a 8.620e-02 1.900e-04 2.188e-01ARPR 2 no d1.5a 8.506e-02 -9.500e-04 -1.108e+00ARPR 1 yes d1.5a 6.581e-02 -2.369e-02 -2.647e+01ARPR 2 yes d1.5a 6.465e-02 -2.485e-02 -2.776e+01ARPR 1 no d2.6 8.701e-02 -8.009e-02 -4.793e+01ARPR 1 yes d2.6 6.663e-02 -1.241e-01 -6.506e+01ARPR 1 no d2.7 7.744e-02 -7.368e-02 -4.876e+01ARPR 2 no d2.7 1.313e-01 -1.984e-02 -1.313e+01ARPR 1 yes d2.7 6.633e-02 -1.239e-01 -6.514e+01ARPR 2 yes d2.7 1.220e-01 -6.829e-02 -3.589e+01

Table B.21.: Variance estimator of the RMPG

V def adj design avgV biasV relbiasV%RMPG 1 no d1.2 4.080e-01 5.260e-03 1.306e+00RMPG 2 no d1.2 4.081e-01 5.330e-03 1.323e+00RMPG 1 yes d1.2 3.327e-01 -1.082e-01 -2.454e+01RMPG 2 yes d1.2 3.328e-01 -1.081e-01 -2.453e+01RMPG 1 no d1.4a 4.140e-01 4.281e-02 1.154e+01RMPG 2 no d1.4a 4.101e-01 3.893e-02 1.049e+01RMPG 1 yes d1.4a 3.231e-01 -7.388e-02 -1.861e+01RMPG 2 yes d1.4a 3.197e-01 -7.730e-02 -1.947e+01RMPG 1 no d1.5a 4.684e-01 -3.870e-03 -8.200e-01RMPG 2 no d1.5a 4.636e-01 -8.630e-03 -1.828e+00RMPG 1 yes d1.5a 3.353e-01 -1.396e-01 -2.940e+01RMPG 2 yes d1.5a 3.312e-01 -1.437e-01 -3.025e+01RMPG 1 no d2.6 4.704e-01 -3.107e-01 -3.977e+01RMPG 1 yes d2.6 3.400e-01 -4.709e-01 -5.807e+01RMPG 1 no d2.7 4.100e-01 -2.902e-01 -4.144e+01RMPG 2 no d2.7 6.147e-01 -8.544e-02 -1.220e+01RMPG 1 yes d2.7 3.236e-01 -4.802e-01 -5.974e+01RMPG 2 yes d2.7 4.949e-01 -3.089e-01 -3.843e+01




Table B.22.: Variance estimator of the QSR

V def adj design avgV biasV relbiasV%QSR 1 no d1.2 1.040e-01 2.090e-03 2.053e+00QSR 2 no d1.2 1.040e-01 2.110e-03 2.071e+00QSR 1 yes d1.2 6.399e-02 -1.797e-02 -2.192e+01QSR 2 yes d1.2 6.400e-02 -1.796e-02 -2.191e+01QSR 1 no d1.4a 1.046e-01 1.151e-02 1.237e+01QSR 2 no d1.4a 1.027e-01 9.620e-03 1.034e+01QSR 1 yes d1.4a 6.357e-02 -7.020e-03 -9.946e+00QSR 2 yes d1.4a 6.229e-02 -8.300e-03 -1.175e+01QSR 1 no d1.5a 1.132e-01 1.270e-03 1.133e+00QSR 2 no d1.5a 1.111e-01 -8.200e-04 -7.312e-01QSR 1 yes d1.5a 6.282e-02 -2.107e-02 -2.512e+01QSR 2 yes d1.5a 6.144e-02 -2.245e-02 -2.676e+01QSR 1 no d2.6 1.128e-01 -1.655e-01 -5.947e+01QSR 1 yes d2.6 6.272e-02 -1.559e-01 -7.131e+01QSR 1 no d2.7 1.040e-01 -1.633e-01 -6.108e+01QSR 2 no d2.7 2.359e-01 -3.143e-02 -1.176e+01QSR 1 yes d2.7 6.278e-02 -1.604e-01 -7.187e+01QSR 2 yes d2.7 1.530e-01 -7.017e-02 -3.144e+01

Table B.23.: Variance estimator of the Gini

V def adj design avgV biasV relbiasV%Gini 1 no d1.2 2e-05 0e+00 -1.983e+01Gini 2 no d1.2 2e-05 0e+00 -1.982e+01Gini 1 yes d1.2 1e-05 -1e-05 -2.593e+01Gini 2 yes d1.2 1e-05 -1e-05 -2.591e+01Gini 1 no d1.4a 2e-05 1e-05 6.176e+01Gini 2 no d1.4a 2e-05 1e-05 5.854e+01Gini 1 yes d1.4a 1e-05 0e+00 4.857e+01Gini 2 yes d1.4a 1e-05 0e+00 4.550e+01Gini 1 no d1.5a 2e-05 1e-05 5.122e+01Gini 2 no d1.5a 1e-05 0e+00 4.776e+01Gini 1 yes d1.5a 1e-05 0e+00 3.089e+01Gini 2 yes d1.5a 1e-05 0e+00 2.761e+01Gini 1 no d2.6 2e-05 -2e-05 -6.197e+01Gini 1 yes d2.6 1e-05 -4e-05 -7.369e+01Gini 1 no d2.7 2e-05 -2e-05 -5.964e+01Gini 2 no d2.7 4e-05 0e+00 -2.967e+00Gini 1 yes d2.7 1e-05 -4e-05 -7.030e+01Gini 2 yes d2.7 4e-05 -1e-05 -2.674e+01



B.2.6. Point estimates of the fitted GB2 parameters, simulationtype 2 of Table B.5


reg: if the parameter was fitted on the global (0) or regional (regions 1-4 of the AMELIAuniverse),

Note that for design d2.6, we were not able to calculate variance estimators using thewhole design information, thus the values in the tables are equal to 0.




Tab

leB

.24.

:P

oint

esti

mat

orofa

Tre

gdes

ign

avgT

mad

Tva

rTcv

sTcv

Tcv

dT

a0

d1.

23.

955e

+00

3.51

4e-0

11.

282e

-01

9.05

3e-0

28.

867e

-02

8.84

2e-0

2a

1d1.

23.

230e

+00

6.02

1e-0

13.

584e

-01

1.85

4e-0

11.

714e

-01

1.71

5e-0

1a

2d1.

26.

220e

+00

1.04

6e+

001.

159e

+00

1.73

1e-0

12.

037e

-01

2.03

7e-0

1a

3d1.

26.

863e

+00

1.15

1e+

001.

324e

+00

1.67

7e-0

12.

197e

-01

2.19

8e-0

1a

4d1.

26.

238e

+00

9.98

3e-0

11.

236e

+00

1.78

2e-0

12.

017e

-01

2.01

7e-0

1a

0d1.

4a3.

960e

+00

3.49

6e-0

11.

217e

-01

8.80

7e-0

28.

851e

-02

8.82

6e-0

2a

1d1.

4a3.

199e

+00

5.59

5e-0

13.

282e

-01

1.79

1e-0

11.

715e

-01

1.71

6e-0

1a

2d1.

4a6.

239e

+00

1.02

8e+

001.

312e

+00

1.83

6e-0

12.

046e

-01

2.04

7e-0

1a

3d1.

4a6.

922e

+00

1.20

3e+

001.

408e

+00

1.71

4e-0

12.

213e

-01

2.21

4e-0

1a

4d1.

4a6.

199e

+00

1.04

0e+

001.

216e

+00

1.77

9e-0

11.

999e

-01

2.00

0e-0

1a

0d1.

5a3.

942e

+00

3.31

1e-0

11.

152e

-01

8.61

0e-0

28.

004e

-02

7.96

9e-0

2a

1d1.

5a3.

209e

+00

4.82

8e-0

12.

713e

-01

1.62

3e-0

11.

559e

-01

1.55

8e-0

1a

2d1.

5a6.

204e

+00

9.84

1e-0

19.

880e

-01

1.60

2e-0

11.

778e

-01

1.77

7e-0

1a

3d1.

5a6.

848e

+00

1.04

9e+

001.

153e

+00

1.56

8e-0

11.

971e

-01

1.96

9e-0

1a

4d1.

5a6.

150e

+00

9.23

8e-0

19.

248e

-01

1.56

4e-0

11.

780e

-01

1.77

9e-0

1a

0d2.

63.

984e

+00

4.10

8e-0

11.

544e

-01

9.86

3e-0

28.

027e

-02

0.00

0e+

00a

1d2.

63.

174e

+00

5.38

8e-0

13.

049e

-01

1.74

0e-0

11.

621e

-01

0.00

0e+

00a

2d2.

66.

182e

+00

9.61

7e-0

18.

920e

-01

1.52

8e-0

11.

765e

-01

0.00

0e+

00a

3d2.

66.

878e

+00

1.18

5e+

001.

230e

+00

1.61

3e-0

11.

979e

-01

0.00

0e+

00a

4d2.

66.

182e

+00

8.92

5e-0

18.

158e

-01

1.46

1e-0

11.

776e

-01

0.00

0e+

00a

0d2.

73.

988e

+00

4.32

3e-0

11.

828e

-01

1.07

2e-0

18.

861e

-02

8.83

6e-0

2a

1d2.

73.

192e

+00

5.35

1e-0

13.

303e

-01

1.80

1e-0

11.

790e

-01

1.70

9e-0

1a

2d2.

76.

232e

+00

1.05

4e+

001.

201e

+00

1.75

9e-0

12.

041e

-01

2.03

9e-0

1a

3d2.

76.

909e

+00

1.26

0e+

001.

562e

+00

1.80

9e-0

12.

184e

-01

2.17

1e-0

1a

4d2.

76.

213e

+00

1.02

0e+

001.

297e

+00

1.83

3e-0

12.

013e

-01

2.00

8e-0

1



Tab

leB

.25.:P

oint

estimator

ofb

Treg

design

avgT

mad

TvarT

cvsT

cvT

cvdT

b0

d1.2

4.648e+04

2.087e+03

5.438e+06

5.017e-024.756e-02

4.735e-02b

1d1.2

3.174e+04

3.707e+03

2.091e+07

1.441e-011.187e-01

1.188e-01b

2d1.2

3.289e+04

1.684e+03

3.052e+06

5.312e-025.647e-02

5.649e-02b

3d1.2

4.359e+04

1.960e+03

4.591e+06

4.915e-025.054e-02

5.056e-02b

4d1.2

5.852e+04

3.346e+03

1.337e+07

6.248e-026.524e-02

6.526e-02b

0d1.4a

4.638e+04

2.174e+03

4.769e+06

4.708e-024.738e-02

4.718e-02b

1d1.4a

3.179e+04

3.702e+03

1.823e+07

1.343e-011.198e-01

1.199e-01b

2d1.4a

3.276e+04

1.706e+03

3.343e+06

5.581e-025.640e-02

5.642e-02b

3d1.4a

4.359e+04

2.019e+03

4.610e+06

4.925e-024.997e-02

4.998e-02b

4d1.4a

5.852e+04

3.346e+03

1.478e+07

6.568e-026.567e-02

6.569e-02b

0d1.5a

4.648e+04

2.097e+03

4.758e+06

4.693e-024.348e-02

4.321e-02b

1d1.5a

3.165e+04

3.128e+03

1.507e+07

1.227e-011.083e-01

1.082e-01b

2d1.5a

3.281e+04

1.547e+03

2.861e+06

5.155e-025.015e-02

5.012e-02b

3d1.5a

4.351e+04

1.772e+03

3.404e+06

4.241e-024.503e-02

4.500e-02b

4d1.5a

5.871e+04

3.251e+03

1.216e+07

5.939e-025.930e-02

5.926e-02b

0d2.6

4.641e+04

2.139e+03

4.739e+06

4.691e-024.304e-02

0.000e+00

b1

d2.6

3.219e+04

3.642e+03

1.978e+07

1.382e-011.167e-01

0.000e+00

b2

d2.6

3.279e+04

1.468e+03

2.439e+06

4.763e-024.964e-02

0.000e+00

b3

d2.6

4.347e+04

1.814e+03

3.624e+06

4.380e-024.494e-02

0.000e+00

b4

d2.6

5.842e+04

3.028e+03

1.126e+07

5.744e-025.872e-02

0.000e+00

b0

d2.7

4.637e+04

2.292e+03

5.749e+06

5.170e-024.739e-02

4.718e-02b

1d2.7

3.216e+04

3.825e+03

2.143e+07

1.440e-011.264e-01

1.219e-01b

2d2.7

3.282e+04

1.678e+03

3.296e+06

5.531e-025.617e-02

5.606e-02b

3d2.7

4.354e+04

1.976e+03

4.325e+06

4.776e-025.022e-02

4.987e-02b

4d2.7

5.865e+04

3.518e+03

1.616e+07

6.855e-026.543e-02

6.519e-02




Tab

leB

.26.

:P

oint

esti

mat

orofp

Tre

gdes

ign

avgT

mad

Tva

rTcv

sTcv

Tcv

dT

p0

d1.

23.

103e

-01

3.22

4e-0

21.

012e

-03

1.02

6e-0

19.

867e

-02

9.85

2e-0

2p

1d1.

23.

843e

-01

8.05

2e-0

26.

165e

-03

2.04

3e-0

11.

953e

-01

1.95

4e-0

1p

2d1.

22.

146e

-01

3.91

7e-0

21.

550e

-03

1.83

4e-0

12.

161e

-01

2.16

2e-0

1p

3d1.

22.

355e

-01

4.44

9e-0

22.

072e

-03

1.93

3e-0

12.

399e

-01

2.40

0e-0

1p

4d1.

22.

254e

-01

3.99

2e-0

21.

768e

-03

1.86

5e-0

12.

160e

-01

2.16

1e-0

1p

0d1.

4a3.

099e

-01

3.17

6e-0

29.

391e

-04

9.88

8e-0

29.

848e

-02

9.83

3e-0

2p

1d1.

4a3.

875e

-01

7.62

8e-0

26.

055e

-03

2.00

8e-0

11.

957e

-01

1.95

8e-0

1p

2d1.

4a2.

152e

-01

3.98

4e-0

21.

604e

-03

1.86

1e-0

12.

170e

-01

2.17

1e-0

1p

3d1.

4a2.

336e

-01

4.37

6e-0

22.

001e

-03

1.91

4e-0

12.

419e

-01

2.42

0e-0

1p

4d1.

4a2.

266e

-01

4.08

9e-0

21.

695e

-03

1.81

7e-0

12.

143e

-01

2.14

4e-0

1p

0d1.

5a3.

113e

-01

3.23

3e-0

29.

859e

-04

1.00

9e-0

19.

082e

-02

9.05

7e-0

2p

1d1.

5a3.

836e

-01

6.93

7e-0

25.

003e

-03

1.84

4e-0

11.

811e

-01

1.80

9e-0

1p

2d1.

5a2.

145e

-01

3.76

7e-0

21.

393e

-03

1.74

0e-0

11.

922e

-01

1.92

0e-0

1p

3d1.

5a2.

355e

-01

4.13

2e-0

21.

886e

-03

1.84

4e-0

12.

214e

-01

2.21

2e-0

1p

4d1.

5a2.

266e

-01

3.73

2e-0

21.

539e

-03

1.73

1e-0

11.

957e

-01

1.95

6e-0

1p

0d2.

63.

096e

-01

3.37

1e-0

21.

044e

-03

1.04

4e-0

19.

106e

-02

0.00

0e+

00p

1d2.

63.

901e

-01

7.76

3e-0

25.

889e

-03

1.96

7e-0

11.

884e

-01

0.00

0e+

00p

2d2.

62.

149e

-01

3.63

0e-0

21.

213e

-03

1.62

0e-0

11.

908e

-01

0.00

0e+

00p

3d2.

62.

353e

-01

4.27

3e-0

21.

953e

-03

1.87

8e-0

12.

220e

-01

0.00

0e+

00p

4d2.

62.

255e

-01

3.62

5e-0

21.

290e

-03

1.59

3e-0

11.

951e

-01

0.00

0e+

00p

0d2.

73.

103e

-01

3.46

7e-0

21.

238e

-03

1.13

4e-0

19.

856e

-02

9.84

1e-0

2p

1d2.

73.

889e

-01

7.23

3e-0

26.

183e

-03

2.02

2e-0

12.

043e

-01

1.95

1e-0

1p

2d2.

72.

152e

-01

3.95

0e-0

21.

499e

-03

1.79

9e-0

12.

164e

-01

2.16

1e-0

1p

3d2.

72.

355e

-01

4.54

3e-0

22.

272e

-03

2.02

4e-0

12.

386e

-01

2.37

0e-0

1p

4d2.

72.

267e

-01

4.09

3e-0

21.

835e

-03

1.88

9e-0

12.

161e

-01

2.15

4e-0

1



Tab

leB

.27.:P

oint

estimator

ofq

Treg

design

avgT

mad

TvarT

cvsT

cvT

cvdT

q0

d1.2

1.135e+00

1.755e-013.533e-02

1.656e-011.566e-01

1.563e-01q

1d1.2

1.419e+00

4.378e-012.985e-01

3.852e-013.198e-01

3.199e-01q

2d1.2

6.416e-011.503e-01

2.595e-022.511e-01

2.888e-012.889e-01

q3

d1.2

6.261e-011.344e-01

2.671e-022.610e-01

3.034e-013.036e-01

q4

d1.2

8.437e-012.146e-01

6.087e-022.924e-01

3.167e-013.168e-01

q0

d1.4a

1.129e+00

1.805e-013.126e-02

1.565e-011.562e-01

1.560e-01q

1d1.4a

1.420e+00

4.296e-012.642e-01

3.618e-013.210e-01

3.211e-01q

2d1.4a

6.394e-011.504e-01

2.809e-022.621e-01

2.896e-012.897e-01

q3

d1.4a

6.209e-011.451e-01

2.735e-022.664e-01

3.040e-013.041e-01

q4

d1.4a

8.510e-012.243e-01

6.489e-022.993e-01

3.157e-013.158e-01

q0

d1.5a

1.139e+00

1.791e-013.261e-02

1.586e-011.437e-01

1.433e-01q

1d1.5a

1.400e+00

3.620e-012.275e-01

3.406e-012.957e-01

2.955e-01q

2d1.5a

6.399e-011.432e-01

2.485e-022.464e-01

2.566e-012.564e-01

q3

d1.5a

6.221e-011.331e-01

2.122e-022.342e-01

2.742e-012.741e-01

q4

d1.5a

8.540e-012.069e-01

5.660e-022.786e-01

2.856e-012.854e-01

q0

d2.6

1.126e+00

1.958e-013.519e-02

1.666e-011.434e-01

0.000e+00

q1

d2.6

1.456e+00

4.273e-012.945e-01

3.726e-013.122e-01

0.000e+00

q2

d2.6

6.360e-011.390e-01

2.000e-022.224e-01

2.543e-010.000e+

00q

3d2.6

6.198e-011.391e-01

2.335e-022.465e-01

2.751e-010.000e+

00q

4d2.6

8.375e-011.989e-01

5.014e-022.674e-01

2.843e-010.000e+

00q

0d2.7

1.128e+00

1.978e-014.109e-02

1.797e-011.564e-01

1.561e-01q

1d2.7

1.447e+00

4.408e-012.974e-01

3.768e-013.370e-01

3.215e-01q

2d2.7

6.425e-011.535e-01

2.758e-022.585e-01

2.892e-012.885e-01

q3

d2.7

6.259e-011.491e-01

2.826e-022.686e-01

3.016e-013.000e-01

q4

d2.7

8.541e-012.322e-01

7.245e-023.152e-01

3.166e-013.151e-01




B.2.7. Variance estimates of the fitted GB2 parameters,simulation type 2 of Table B.5

In Tables B.28, B.29, B.30 and B.31 the used notation is as for the parameters.



Table B.28.: Variance estimator of a

V def reg design avgV biasV relbiasV%a 1 0 d1.2 1.268e-01 -1.420e-03 -1.106e+00a 2 0 d1.2 1.261e-01 -2.140e-03 -1.666e+00a 1 1 d1.2 3.516e-01 -6.820e-03 -1.902e+00a 2 1 d1.2 3.519e-01 -6.580e-03 -1.837e+00a 1 2 d1.2 2.036e+00 8.772e-01 7.569e+01a 2 2 d1.2 2.037e+00 8.783e-01 7.578e+01a 1 3 d1.2 2.769e+00 1.445e+00 1.091e+02a 2 3 d1.2 2.771e+00 1.447e+00 1.093e+02a 1 4 d1.2 2.124e+00 8.883e-01 7.189e+01a 2 4 d1.2 2.125e+00 8.897e-01 7.200e+01a 1 0 d1.4a 1.264e-01 4.710e-03 3.872e+00a 2 0 d1.4a 1.257e-01 4.000e-03 3.291e+00a 1 1 d1.4a 3.388e-01 1.066e-02 3.248e+00a 2 1 d1.4a 3.391e-01 1.089e-02 3.317e+00a 1 2 d1.4a 2.118e+00 8.060e-01 6.145e+01a 2 2 d1.4a 2.119e+00 8.072e-01 6.154e+01a 1 3 d1.4a 3.004e+00 1.596e+00 1.134e+02a 2 3 d1.4a 3.006e+00 1.598e+00 1.135e+02a 1 4 d1.4a 1.974e+00 7.580e-01 6.233e+01a 2 4 d1.4a 1.975e+00 7.591e-01 6.242e+01a 1 0 d1.5a 1.017e-01 -1.355e-02 -1.176e+01a 2 0 d1.5a 1.008e-01 -1.444e-02 -1.253e+01a 1 1 d1.5a 2.738e-01 2.500e-03 9.210e-01a 2 1 d1.5a 2.734e-01 2.100e-03 7.759e-01a 1 2 d1.5a 1.450e+00 4.621e-01 4.677e+01a 2 2 d1.5a 1.448e+00 4.599e-01 4.654e+01a 1 3 d1.5a 2.085e+00 9.315e-01 8.075e+01a 2 3 d1.5a 2.082e+00 9.287e-01 8.052e+01a 1 4 d1.5a 1.412e+00 4.868e-01 5.264e+01a 2 4 d1.5a 1.410e+00 4.848e-01 5.242e+01a 1 0 d2.6 1.047e-01 -4.965e-02 -3.216e+01a 1 1 d2.6 2.972e-01 -7.730e-03 -2.533e+00a 1 2 d2.6 1.430e+00 5.381e-01 6.032e+01a 1 3 d2.6 2.202e+00 9.715e-01 7.897e+01a 1 4 d2.6 1.384e+00 5.680e-01 6.963e+01a 1 0 d2.7 1.293e-01 -5.346e-02 -2.925e+01a 2 0 d2.7 1.286e-01 -5.416e-02 -2.963e+01a 1 1 d2.7 3.818e-01 5.152e-02 1.560e+01a 2 1 d2.7 3.678e-01 3.751e-02 1.136e+01a 1 2 d2.7 2.179e+00 9.777e-01 8.139e+01a 2 2 d2.7 2.225e+00 1.024e+00 8.527e+01a 1 3 d2.7 2.876e+00 1.314e+00 8.410e+01a 2 3 d2.7 2.914e+00 1.352e+00 8.653e+01a 1 4 d2.7 2.174e+00 8.762e-01 6.754e+01a 2 4 d2.7 2.232e+00 9.346e-01 7.204e+01




Table B.29.: Variance estimator of b

V def reg design avgV biasV relbiasV%b 1 0 d1.2 1.268e-01 -1.420e-03 -1.106e+00b 2 0 d1.2 1.261e-01 -2.140e-03 -1.666e+00b 1 1 d1.2 3.516e-01 -6.820e-03 -1.902e+00b 2 1 d1.2 3.519e-01 -6.580e-03 -1.837e+00b 1 2 d1.2 2.036e+00 8.772e-01 7.569e+01b 2 2 d1.2 2.037e+00 8.783e-01 7.578e+01b 1 3 d1.2 2.769e+00 1.445e+00 1.091e+02b 2 3 d1.2 2.771e+00 1.447e+00 1.093e+02b 1 4 d1.2 2.124e+00 8.883e-01 7.189e+01b 2 4 d1.2 2.125e+00 8.897e-01 7.200e+01b 1 0 d1.4a 1.264e-01 4.710e-03 3.872e+00b 2 0 d1.4a 1.257e-01 4.000e-03 3.291e+00b 1 1 d1.4a 3.388e-01 1.066e-02 3.248e+00b 2 1 d1.4a 3.391e-01 1.089e-02 3.317e+00b 1 2 d1.4a 2.118e+00 8.060e-01 6.145e+01b 2 2 d1.4a 2.119e+00 8.072e-01 6.154e+01b 1 3 d1.4a 3.004e+00 1.596e+00 1.134e+02b 2 3 d1.4a 3.006e+00 1.598e+00 1.135e+02b 1 4 d1.4a 1.974e+00 7.580e-01 6.233e+01b 2 4 d1.4a 1.975e+00 7.591e-01 6.242e+01b 1 0 d1.5a 1.017e-01 -1.355e-02 -1.176e+01b 2 0 d1.5a 1.008e-01 -1.444e-02 -1.253e+01b 1 1 d1.5a 2.738e-01 2.500e-03 9.210e-01b 2 1 d1.5a 2.734e-01 2.100e-03 7.759e-01b 1 2 d1.5a 1.450e+00 4.621e-01 4.677e+01b 2 2 d1.5a 1.448e+00 4.599e-01 4.654e+01b 1 3 d1.5a 2.085e+00 9.315e-01 8.075e+01b 2 3 d1.5a 2.082e+00 9.287e-01 8.052e+01b 1 4 d1.5a 1.412e+00 4.868e-01 5.264e+01b 2 4 d1.5a 1.410e+00 4.848e-01 5.242e+01b 1 0 d2.6 1.047e-01 -4.965e-02 -3.216e+01b 1 1 d2.6 2.972e-01 -7.730e-03 -2.533e+00b 1 2 d2.6 1.430e+00 5.381e-01 6.032e+01b 1 3 d2.6 2.202e+00 9.715e-01 7.897e+01b 1 4 d2.6 1.384e+00 5.680e-01 6.963e+01b 1 0 d2.7 1.293e-01 -5.346e-02 -2.925e+01b 2 0 d2.7 1.286e-01 -5.416e-02 -2.963e+01b 1 1 d2.7 3.818e-01 5.152e-02 1.560e+01b 2 1 d2.7 3.678e-01 3.751e-02 1.136e+01b 1 2 d2.7 2.179e+00 9.777e-01 8.139e+01b 2 2 d2.7 2.225e+00 1.024e+00 8.527e+01b 1 3 d2.7 2.876e+00 1.314e+00 8.410e+01b 2 3 d2.7 2.914e+00 1.352e+00 8.653e+01b 1 4 d2.7 2.174e+00 8.762e-01 6.754e+01b 2 4 d2.7 2.232e+00 9.346e-01 7.204e+01



Table B.30.: Variance estimator of p

V def reg design avgV biasV relbiasV%p 1 0 d1.2 1.268e-01 -1.420e-03 -1.106e+00p 2 0 d1.2 1.261e-01 -2.140e-03 -1.666e+00p 1 1 d1.2 3.516e-01 -6.820e-03 -1.902e+00p 2 1 d1.2 3.519e-01 -6.580e-03 -1.837e+00p 1 2 d1.2 2.036e+00 8.772e-01 7.569e+01p 2 2 d1.2 2.037e+00 8.783e-01 7.578e+01p 1 3 d1.2 2.769e+00 1.445e+00 1.091e+02p 2 3 d1.2 2.771e+00 1.447e+00 1.093e+02p 1 4 d1.2 2.124e+00 8.883e-01 7.189e+01p 2 4 d1.2 2.125e+00 8.897e-01 7.200e+01p 1 0 d1.4a 1.264e-01 4.710e-03 3.872e+00p 2 0 d1.4a 1.257e-01 4.000e-03 3.291e+00p 1 1 d1.4a 3.388e-01 1.066e-02 3.248e+00p 2 1 d1.4a 3.391e-01 1.089e-02 3.317e+00p 1 2 d1.4a 2.118e+00 8.060e-01 6.145e+01p 2 2 d1.4a 2.119e+00 8.072e-01 6.154e+01p 1 3 d1.4a 3.004e+00 1.596e+00 1.134e+02p 2 3 d1.4a 3.006e+00 1.598e+00 1.135e+02p 1 4 d1.4a 1.974e+00 7.580e-01 6.233e+01p 2 4 d1.4a 1.975e+00 7.591e-01 6.242e+01p 1 0 d1.5a 1.017e-01 -1.355e-02 -1.176e+01p 2 0 d1.5a 1.008e-01 -1.444e-02 -1.253e+01p 1 1 d1.5a 2.738e-01 2.500e-03 9.210e-01p 2 1 d1.5a 2.734e-01 2.100e-03 7.759e-01p 1 2 d1.5a 1.450e+00 4.621e-01 4.677e+01p 2 2 d1.5a 1.448e+00 4.599e-01 4.654e+01p 1 3 d1.5a 2.085e+00 9.315e-01 8.075e+01p 2 3 d1.5a 2.082e+00 9.287e-01 8.052e+01p 1 4 d1.5a 1.412e+00 4.868e-01 5.264e+01p 2 4 d1.5a 1.410e+00 4.848e-01 5.242e+01p 1 0 d2.6 1.047e-01 -4.965e-02 -3.216e+01p 1 1 d2.6 2.972e-01 -7.730e-03 -2.533e+00p 1 2 d2.6 1.430e+00 5.381e-01 6.032e+01p 1 3 d2.6 2.202e+00 9.715e-01 7.897e+01p 1 4 d2.6 1.384e+00 5.680e-01 6.963e+01p 1 0 d2.7 1.293e-01 -5.346e-02 -2.925e+01p 2 0 d2.7 1.286e-01 -5.416e-02 -2.963e+01p 1 1 d2.7 3.818e-01 5.152e-02 1.560e+01p 2 1 d2.7 3.678e-01 3.751e-02 1.136e+01p 1 2 d2.7 2.179e+00 9.777e-01 8.139e+01p 2 2 d2.7 2.225e+00 1.024e+00 8.527e+01p 1 3 d2.7 2.876e+00 1.314e+00 8.410e+01p 2 3 d2.7 2.914e+00 1.352e+00 8.653e+01p 1 4 d2.7 2.174e+00 8.762e-01 6.754e+01p 2 4 d2.7 2.232e+00 9.346e-01 7.204e+01




Table B.31.: Variance estimator of q

V def reg design avgV biasV relbiasV%q 1 0 d1.2 1.268e-01 -1.420e-03 -1.106e+00q 2 0 d1.2 1.261e-01 -2.140e-03 -1.666e+00q 1 1 d1.2 3.516e-01 -6.820e-03 -1.902e+00q 2 1 d1.2 3.519e-01 -6.580e-03 -1.837e+00q 1 2 d1.2 2.036e+00 8.772e-01 7.569e+01q 2 2 d1.2 2.037e+00 8.783e-01 7.578e+01q 1 3 d1.2 2.769e+00 1.445e+00 1.091e+02q 2 3 d1.2 2.771e+00 1.447e+00 1.093e+02q 1 4 d1.2 2.124e+00 8.883e-01 7.189e+01q 2 4 d1.2 2.125e+00 8.897e-01 7.200e+01q 1 0 d1.4a 1.264e-01 4.710e-03 3.872e+00q 2 0 d1.4a 1.257e-01 4.000e-03 3.291e+00q 1 1 d1.4a 3.388e-01 1.066e-02 3.248e+00q 2 1 d1.4a 3.391e-01 1.089e-02 3.317e+00q 1 2 d1.4a 2.118e+00 8.060e-01 6.145e+01q 2 2 d1.4a 2.119e+00 8.072e-01 6.154e+01q 1 3 d1.4a 3.004e+00 1.596e+00 1.134e+02q 2 3 d1.4a 3.006e+00 1.598e+00 1.135e+02q 1 4 d1.4a 1.974e+00 7.580e-01 6.233e+01q 2 4 d1.4a 1.975e+00 7.591e-01 6.242e+01q 1 0 d1.5a 1.017e-01 -1.355e-02 -1.176e+01q 2 0 d1.5a 1.008e-01 -1.444e-02 -1.253e+01q 1 1 d1.5a 2.738e-01 2.500e-03 9.210e-01q 2 1 d1.5a 2.734e-01 2.100e-03 7.759e-01q 1 2 d1.5a 1.450e+00 4.621e-01 4.677e+01q 2 2 d1.5a 1.448e+00 4.599e-01 4.654e+01q 1 3 d1.5a 2.085e+00 9.315e-01 8.075e+01q 2 3 d1.5a 2.082e+00 9.287e-01 8.052e+01q 1 4 d1.5a 1.412e+00 4.868e-01 5.264e+01q 2 4 d1.5a 1.410e+00 4.848e-01 5.242e+01q 1 0 d2.6 1.047e-01 -4.965e-02 -3.216e+01q 1 1 d2.6 2.972e-01 -7.730e-03 -2.533e+00q 1 2 d2.6 1.430e+00 5.381e-01 6.032e+01q 1 3 d2.6 2.202e+00 9.715e-01 7.897e+01q 1 4 d2.6 1.384e+00 5.680e-01 6.963e+01q 1 0 d2.7 1.293e-01 -5.346e-02 -2.925e+01q 2 0 d2.7 1.286e-01 -5.416e-02 -2.963e+01q 1 1 d2.7 3.818e-01 5.152e-02 1.560e+01q 2 1 d2.7 3.678e-01 3.751e-02 1.136e+01q 1 2 d2.7 2.179e+00 9.777e-01 8.139e+01q 2 2 d2.7 2.225e+00 1.024e+00 8.527e+01q 1 3 d2.7 2.876e+00 1.314e+00 8.410e+01q 2 3 d2.7 2.914e+00 1.352e+00 8.653e+01q 1 4 d2.7 2.174e+00 8.762e-01 6.754e+01q 2 4 d2.7 2.232e+00 9.346e-01 7.204e+01



B.2.8. Point estimates of the fitted GB2 indicators, simulationtype 2 of Table B.5





Tab

leB

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:P

oint

esti

mat

orof

the

med

ian

Tre

gdes

ign

avgT

mad

Tva

rTcv

sTcv

Tcv

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edia

n0

d1.

22.

588e

+04

3.17

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537e

+04

1.12

9e-0

21.

166e

-02

1.08

2e-0

21.

213e

+00

Med

ian

1d1.

21.

627e

+04

4.10

7e+

021.

658e

+05

2.50

3e-0

22.

530e

-02

2.53

1e-0

21.

812e

+00

Med

ian

2d1.

22.

179e

+04

4.12

4e+

021.

721e

+05

1.90

4e-0

21.

922e

-02

1.92

2e-0

27.

557e

-01

Med

ian

3d1.

23.

156e

+04

5.74

1e+

023.

269e

+05

1.81

2e-0

21.

866e

-02

1.86

6e-0

25.

376e

-01

Med

ian

4d1.

23.

704e

+04

7.12

8e+

024.

846e

+05

1.88

0e-0

21.

865e

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1.86

5e-0

2-5

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Med

ian

0d1.

4a2.

588e

+04

2.54

1e+

027.

604e

+04

1.06

5e-0

21.

164e

-02

1.08

0e-0

21.

191e

+00

Med

ian

1d1.

4a1.

appendix to the report on the simulation results · 2013. 8. 18. · evaluation oliver bode,...

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