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STM JOURNALSScientific Technical Medical

www.stmjournals.com

Jan - April 2014

(RRJoST)ISSN : 2348-7909

Research & Reviews Journal of Statistics

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Industrial Tribology Machine Dynamics & Maintenance

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STM JOURNALS

1. Estimation of Mean with Imputation of Missing Data in Stratified Random Sampling Narendra Singh Thakur, Kalpana Yadav, Sharad Pathak 1

2. Hybrid Poisson Distribution Sampath Sundaram, Deepa S P 13

3. Individual Patient Data Meta-Analysis using Proportional Hazard ModelsMd. Nuruzzaman Forhad, Md. Erfanul Hoque, Md. Belal Hossain 23

4. A New Form of Sam-Solai's Multivariate Generalized Normal DistributionG.S. David Sam Jayakumar, A. Solairaju, A. Sulthan 33

ContentsResearch & Reviews : Journal of Statistics

RRJoST (2014)© STM Journals 2014. All Rights Reserved

Research & Reviews: Journal of Statistics ISSN: 2348-7909

Volume 3, Issue 1

www.stmjournals.com

Estimation of Mean with Imputation of Missing Data

in Stratified Random Sampling

Narendra Singh Thakur1*, Kalpana Yadav

2, Sharad Pathak

3

1Department of Mathematics and Statistics, Banasthali University, Banasthali, Rajasthan, India

2Department of Statistics, Delhi University, Delhi, India

3Department of Mathematics and Statistics, Dr. H. S. Gour Central Univesity, Sagar (M.P), India

Abstract In this paper we present some imputation methods to estimate the population mean in presence of missing data under stratified sampling design. The suggested methods are

discussed in simple random sampling as well. The expression of bias and MSE are derived in the form of population parameters using the concept of large sample

approximation upto first order. A Comparative study is considered between stratified

and simple random sampling. The empirical study is carried out over two real populations.

Keywords: Estimation, missing data, bias, mean squared error (M.S.E.), stratified

random sampling, SRSWOR, large sample approximation

RRJoST (2014)© STM Journals 2014. All Rights Reserved

Research & Reviews: Journal of Statistics ISSN: 2348-7909

Volume 3, Issue 1

www.stmjournals.com

Hybrid Poisson Distribution

Sampath Sundaram1*, Deepa S P

2

1Department of Statistics, University of Madras, Chennai 600005, India

2Department of Statistics, SDNB Vaishnav College for Women, Chromepet, Chennai, India

Abstract In this paper, hybrid version of Poisson distribution using the Chance Theory due to Liu

(2008) is developed. The process of computing chance values of various events, mean and variance of hybrid poisson distribution using an evolutionary algorithm, namely,

genetic algorithm are discussed with some illustrative examples.

Keywords: Hybrid variable, chance distribution, hybrid binomial distribution, hybrid

poisson distribution

RRJoST (2014) © STM Journals 2014. All Rights Reserved

Research & Reviews: Journal of Statistics ISSN: 2348-7909

Volume 3, Issue 1

www.stmjournals.com

Individual Patient Data Meta-Analysis using Proportional

Hazard Models

Md. Nuruzzaman Forhad1*, Md. Erfanul Hoque

2*, Md. Belal Hossain1

1Department of Statistics, Biostatistics & Informatics, University of Dhaka, Dhaka, Bangladesh

2Department of Statistics, Jagannath University, Dhaka, Bangladesh

Abstract One alternative to classical meta-analytic approaches is known as individual patient data (IPD) meta-analysis. Rather than depending on summary statistics calculated for

individual studies, IPD meta-analysis analyzes the complete data from all included

studies. The IPD meta-analysis is considered the gold-standard for synthesizing survival data. In this paper, an attempt has been made to introduce the use of parametric and

semi-parametric proportional hazard models to perform one and two-step IPD meta-analysis of time-to-event outcomes. Three parametric PH models: exponential PH model,

Weibull PH model, log-logistic PH model and one semi-parametric PH model: Cox PH

model have been used for this purpose. The parameter estimation procedure has been illustrated in two-step approach and finally hazard ratio has been calculated. For the

illustration of the proposed framework, the demographic health survey (DHS) data for

ten countries has been used. An investigation is made to assess the impact of place of residence on child mortality by applying our proposed IPD meta-analysis methods and

finally make a comparison of the rate of child mortality between rural and urban area. Here different studies (different countries) show contradictory results but after

performing proposed meta-analysis approach the actual impact of place of resident on

child mortality has been found. The given approach provides an appropriate guideline to get the better estimated values by using the appropriate model to the data. If the

distribution of the data is known then one can easily gets the appropriate result using this approach.

Keywords: Hazard ratio, individual patient data, proportional hazard model, meta-analysis

RRJoST (2014)© STM Journals 2014. All Rights Reserved

Research & Reviews: Journal of Statistics ISSN: 2348-7909

Volume 3, Issue 1

www.stmjournals.com

A New Form of Sam-Solai’s Multivariate Generalized

Normal Distribution

G.S. David Sam Jayakumar1*, A. Solairaju

2, A. Sulthan

3

Jamal Mohamed College, Tiruchirappalli–620 020, South India, India

Abstract This paper proposed a new generalization of family of Sarmanov type Continuous multivariate symmetric probability distribution with reference to a new form of Sam-

Solai’s Multivariate Generalized normal distribution from univariate case. Further, we find its Marginal, Conditional distributions, Generating functions and also discussed

it’s special cases.The shape parameter played a significance role and it determines the

family of some existing multivariate distributions as subclass of the proposed multivariate generalized normal distribution. The special cases include the

transformation of MVGND into Generalized log-normal distribution and Sam-Solai’s

Multivariate log-Laplace distribution. The following results are redundant: (1) Sam-Solai’s Multivariate Laplace distribution, (2) Sam-Solai’s Multivariate Gaussian

normal distribution, (3) Sam-Solai’s Multivariate mixture of normal-Laplace distribution, (4) Sam-Solai’s Multivariate and (5) Sam-Solai’s Multivariate log-normal

distribution. Moreover, it is found that the conditional variance of Sam-Solai’s

Multivariate generalized conditional normal distribution is heteroskedastic and the correlation co-efficient between any two generalized normal random variables

determined by the shape parameters .Finally, area values of the Bivariate Generalized

normal distribution are extracted and bivariate probability surfaces are visualized for different values of shape parameters.

Keywords: Sarmanov type, Sam-Solai’s, multivariate generalized normal

distribution, conditional variance, heteroskedastic, shape parameter