RNLNL

Generates pseudorandom numbers from a lognormal distribution.

Required Arguments

XM — Mean of the underlying normal distribution. (Input)

S — Standard deviation of the underlying normal distribution. (Input)
S must be positive.

R — Vector of length NR containing the random lognormal deviates. (Output)
The log of each element of R has a normal distribution with mean XM and standard deviation S.

Optional Arguments

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

FORTRAN 90 Interface

Generic: CALL RNLNL (XM, S, R [, …])

Specific: The specific interface names are S_RNLNL and D_RNLNL.

FORTRAN 77 Interface

Single: CALL RNLNL (NR, XM, S, R)

Double: The double precision name is DRNLNL.

Description

Routine RNLNL generates pseudorandom numbers from a lognormal distribution with parameters XM and S. The scale parameter in the underlying normal distribution, S, must be positive. The method is to generate normal deviates with mean XM and standard deviation S and then to exponentiate the normal deviates.

With μ = XM and σ = S, the probability density function for the lognormal distribution is

 

The mean and variance of the lognormal distribution are exp(μ + σ2/2) and exp(2μ + 2σ2) ‑ exp(2μ + σ2), respectively.

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, RNLNL is used to generate five pseudorandom lognormal deviates with μ = 0 and σ = 1.

 

USE RNLNL_INT

USE UMACH_INT

USE RNSET_INT

 

IMPLICIT NONE

INTEGER NR

PARAMETER (NR=5)

!

INTEGER ISEED, NOUT

REAL R(NR), S, XM

!

CALL UMACH (2, NOUT)

XM = 0.0

S = 1.0

ISEED = 123457

CALL RNSET (ISEED)

CALL RNLNL (XM, S, R)

WRITE (NOUT,99999) R

99999 FORMAT (' Lognormal random deviates: ', 5F8.4)

END

Output

 

Lognormal random deviates: 7.7801 2.9543 1.0861 3.5885 0.2935