RNLGR

Generates pseudorandom numbers from a logarithmic distribution.

Required Arguments

A — Parameter of the logarithmic distribution. (Input)
A must be positive and less than 1.0.

IR — Vector of length NR containing the random logarithmic deviates. (Output)

Optional Arguments

NR — Number of random numbers to generate. (Input)
Default: NR = size (IR,1).

FORTRAN 90 Interface

Generic: CALL RNLGR (A, IR [, …])

Specific: The specific interface name is S_RNLGR.

FORTRAN 77 Interface

Single: CALL RNLGR (NR, A, IR)

Description

Routine RNLGR generates pseudorandom numbers from a logarithmic distribution with parameter A. The probability function is

 

for x = 1, 2, 3, …, and 0 < a < 1.

The methods used are described by Kemp (1981) and depend on the value of A. If A is less than 0.95, Kemp’s algorithm LS, which is a “chop‑down” variant of an inverse CDF technique, is used. Otherwise, Kemp’s algorithm LK, which gives special treatment to the highly probable values of 1 and 2, is used.

Comments

The routine RNSET can be used to initialize the seed of the random number generator. The routine RNOPT can be used to select the form of the generator.

Example

In this example, RNLGR is used to generate 5 pseudo‑random deviates from a logarithmic distribution with parameter A equal to 0.3.

 

USE RNLGR_INT

USE UMACH_INT

USE RNSET_INT

 

IMPLICIT NONE

INTEGER NR

PARAMETER (NR=5)

!

INTEGER IR(NR), ISEED, NOUT

REAL A

!

CALL UMACH (2, NOUT)

A = 0.3

ISEED = 123457

CALL RNSET (ISEED)

CALL RNLGR (A, IR)

WRITE (NOUT,99999) IR

99999 FORMAT (' Logarithmic (0.3) random deviates: ', 5I8)

END

Output

 

Logarithmic (0.3) random deviates: 2 1 1 1 2