RNNOA

Generates pseudorandom numbers from a standard normal distribution using an acceptance/rejection method.

Required Arguments

R — Vector of length NR containing the random standard normal deviates. (Output)

Optional Arguments

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

FORTRAN 90 Interface

Generic: CALL RNNOA (R [, …])

Specific: The specific interface names are S_RNNOA and D_RNNOA.

FORTRAN 77 Interface

Single: CALL RNNOA (NR, R)

Double: The double precision name is DRNNOA.

Description

Routine RNNOA generates pseudorandom numbers from a standard normal (Gaussian) distribution using an acceptance/rejection technique due to Kinderman and Ramage (1976). In this method, the normal density is represented as a mixture of densities over which a variety of acceptance/rejection methods due to Marsaglia (1964), Marsaglia and Bray (1964), and Marsaglia, MacLaren, and Bray (1964) are applied. This method is faster than the inverse CDF technique used in RNNOR to generate standard normal deviates.

Deviates from the normal distribution with mean XM and standard deviation XSTD can be obtained by scaling the output from RNNOA. The following statements (in single precision) would yield random deviates from a normal (XM, XSTD**2) distribution.

 

CALL RNNOA (NR, R)

CALL SSCAL (NR, XSTD, R, 1)

CALL SADD (NR, XM, R, 1)

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, RNNOA is used to generate five pseudorandom deviates from a standard normal distribution.

 

USE RNNOA_INT

USE UMACH_INT

USE RNSET_INT

 

IMPLICIT NONE

INTEGER ISEED, NOUT, NR

REAL R(5)

!

CALL UMACH (2, NOUT)

NR = 5

ISEED = 123457

CALL RNSET (ISEED)

CALL RNNOA (R)

WRITE (NOUT,99999) R

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

END

Output

 

Standard normal random deviates: 2.0516 1.0833 0.0826 1.2777 -1.2260