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=== STA 6106 Computer-Intensive Methods in Statistics

Some Sample FOTA! "" #ro$rams ====

The following FORTRAN 77 program calls a random number generating function to generate a

single random number between 0 and 1, using an entered seed value, and entered values of the

generator constants

PROGRAM RANDGENR

PRINT*, 'Enter seed value, and values of A and B:'

READ*, SEED, A, B

PRINT*, 'Random numer !s ', RANDOM"SEED, A, B#

END

$%N&TION RANDOM"(, &ONST, DI)IS#

MOD"&ONST*(,DI)IS#

RANDOM +DI)IS

END

Note that all FORTRAN command lines must begin at column 7 or after, and cannot e!tend past

column 7" The first # columns are reserved for line numbers

The following FORTRAN 77 program generates a list of 100 random numbers between 0 and 1,

using a $O loop

PROGRAM RANDGENR

PRINT*, 'Enter seed value, and values of A and B:'

READ*, SEED, A, B

-

MOD"A*SEED,B#

SEED

DO ./I0E " 10E1 -((#

MOD"A*SEED,B#

RANDOM +B

PRINT*, RANDOM

SEED

2 -

ENDDO

END

The following FORTRAN 77 program uses the %aw of %arge Numbers to appro!imate the

integral 1

0

&dxx , using &000 pseudorandom numbers between 0 and 1 Note that the values of

the generator constants are written into the program' the onl( input is the seed value

PROGRAM RANDGENR

PRINT*, 'Enter seed value: '

READ*, SEED

-

A -34(5

B 6-75748375

MOD"A*SEED,B#

SEED

S%M (

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DO ./I0E " 10E1 6(((#

MOD"A*SEED,B#

RANDOM +B

PRINT*, RANDOM

S%M S%M 2 "RANDOM*RANDOM#

SEED

2 -

ENDDO

S%M S%M+6(((

PRINT*, 'Inte9ral !s aro;!matel< '

PRINT*, S%M

END

The following FORTRAN 77 program uses the %aw of %arge Numbers to appro!imate the

integral ( ) ( )01&

11

0

&

&

=

dze

z

, using &000 generated pseudorandom numbers

PROGRAM STDNORM

REA0 PI PRINT*, 'Enter seed value: '

READ*, SEED

PI 81-7-=>63=7

-

A -34(5

B 6-75748375

MOD"A*SEED,B#

SEED

S%M (

DO ./I0E " 10E1 6(((#

MOD"A*SEED,B#

RANDOM +B

PRINT*, RANDOM

ARGMNT "-+RANDOM# ? -

S%M S%M 2 ""EP"?(1=*"ARGMNT**6###+S@RT"6*PI##+"RANDOM**6#

SEED

2 -

ENDDO

S%M S%M+6(((

PRINT*, 'Inte9ral !s aro;!matel< '

PRINT*, S%M

END

The following FORTRAN 77 program calculates the value of ( ) ( )))

PROGRAM STDNORM

REA0 PI

PRINT*, 'Enter seed value: '

READ*, SEED

PI 81-7-=>63=7

-

A -34(5

B 6-75748375

MOD"A*SEED,B#

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SEED

S%M (

DO ./I0E " 10E1 6(((#

MOD"A*SEED,B#

RANDOM +B

PRINT*, RANDOM

ARGMNT ?7 2 "4*RANDOM#

S%M S%M 2 "4*"EP"?(1=*"ARGMNT**6###+S@RT"6*PI##

SEED

2 -

ENDDO

S%M S%M+6(((

PRINT*, 'Inte9ral !s aro;!matel< '

PRINT*, S%M

END

The following FORTRAN 77 program estimates the value of , using the algorithm discussed in

class Note that the number of pairs of pseudorandom numbers needs to be *uite large to get a

value close to

PROGRAM ESTPI

PRINT*, 'Enter seed values, and samle s!e: '

READ*, SEED-, SEED6, N

A -34(5

B 6-75748375

-

&O%NT (

- MOD"A*SEED-,B#

6 MOD"A*SEED6,B#

SEED- -

SEED6 6

DO ./I0E " 10E1 N# - MOD"A*SEED-,B#

6 MOD"A*SEED6,B#

RANDOM- -+B

RANDOM6 6+B

PRINT*, RANDOM-, RANDOM6

SEED- -

SEED6 6

""6*RANDOM-?-#**6#2""6*RANDOM6?-#**6#

I$ " 10E1 -# &O%NT &O%NT 2 -

2 -

ENDDO

PIEST 7*&O%NT+N

PRINT*, 'Est!mated value of PI ', PIEST END