RNNOR
Generates pseudorandom numbers from a standard normal distribution using an inverse CDF 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 RNNOR (R [, …])
Specific: The specific interface names are S_RNNOR and D_RNNOR.
FORTRAN 77 Interface
Single: CALL RNNOR (NR, R)
Double: The double precision name is DRNNOR.
Description
Routine
RNNOR generates pseudorandom numbers from a standard normal (Gaussian) distribution using an inverse CDF technique. In this method, a uniform (0,1) random deviate is generated and then the inverse of the normal distribution function is evaluated at that point, using the routine
ANORIN (see
Chapter 17, “Probability Distribution Function and Inverses”). This method is slower than the acceptance/rejection technique used in the routine
RNNOA 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
RNNOR. The following statements (in single precision, using the routines
SSCAL (IMSL MATH/LIBRARY) and
SADD (IMSL MATH/LIBRARY).) would yield random deviates from a normal (
XM,
XSTD**2) distribution.
USE IMSL_LIBRARIES
⋮
CALL RNNOR (R, NR)
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, RNNOR is used to generate five pseudorandom deviates from a standard normal distribution.
USE RNNOR_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 RNNOR (R)
WRITE (NOUT,99999) R
99999 FORMAT (' Standard normal random deviates: ', 5F8.4)
END
Output
Standard normal random deviates: 1.8279 -0.6412 0.7266 0.1747 1.0145
