RNWIB
Generates pseudorandom numbers from a Weibull distribution.
Required Arguments
A — The shape parameter of the Weibull distribution. (Input)
This parameter must be positive.
R — Vector of length NR containing the random Weibull deviates. (Output)
Optional Arguments
NR — Number of random numbers to generate. (Input)
Default: NR = size (R,1).
FORTRAN 90 Interface
Generic: CALL RNWIB (A, R [, …])
Specific: The specific interface names are S_RNWIB and D_RNWIB.
FORTRAN 77 Interface
Single: CALL RNWIB (NR, A, R)
Double: The double precision name is DRNWIB.
Description
Routine RNWIB generates pseudorandom numbers from a Weibull distribution with shape parameter A and unit scale parameter. The probability density function is
Routine RNWIB uses an antithetic inverse CDF technique to generate a Weibull variate; that is, a uniform random deviate U is generated and the inverse of the Weibull cumulative distribution function is evaluated at 1.0 ‑ U to yield the Weibull deviate.
Deviates from the two‑parameter Weibull distribution with shape parameter A and scale parameter B can be generated by using RNWIB and then multiplying each entry in R by B. The following statements (using routine SSCAL (IMSL MATH/LIBARY) in single precision) would yield random deviates from a two‑parameter Weibull distribution.
CALL RNWIB (NR, A, R)
CALL SSCAL (NR, B, R, 1)
The Rayleigh distribution with probability density function,
is the same as a Weibull distribution with shape parameter A equal to 2 and scale parameter B equal to
hence, RNWIB and SSCAL (or simple multiplication) can be used to generate Rayleigh deviates.
Comments
1. Informational error
|
Type |
Code |
Description |
|
3 |
1 |
The value of A is so small that the proportion of values from the Weibull that are too large to represent is greater than machine epsilon. |
2. 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, RNWIB is used to generate five pseudorandom deviates from a two‑parameter Weibull distribution with shape parameter equal to 2.0 and scale parameter equal to 6.0, a Rayleigh distribution with parameter
USE RNWIB_INT
USE UMACH_INT
USE RNSET_INT
USE SSCAL_INT
IMPLICIT NONE
INTEGER ISEED, NOUT, NR
REAL A, B, R(5)
!
CALL UMACH (2, NOUT)
A = 2.0
B = 6.0
NR = 5
ISEED = 123457
CALL RNSET (ISEED)
CALL RNWIB (A, R)
CALL SSCAL (NR, B, R, 1)
WRITE (NOUT,99999) R
99999 FORMAT (' Weibull(2,6) random deviates: ', 5F8.4)
END
Output
Weibull(2,6) random deviates: 1.1122 6.9568 3.0959 4.5031 2.4638
