RNGCT

Generates pseudorandom numbers from a general continuous distribution.

Required Arguments

TABLE — NDATA by 5 table to be used for interpolation of the cumulative distribution function. (Input)
The first column of TABLE contains abscissas of the cumulative distribution function in ascending order, the second column contains the values of the CDF (which must be strictly increasing beginning with 0.0 and ending at 1.0) and the remaining columns contain values used in interpolation. This table is set up using routine RNGCS.

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

Optional Arguments

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

NDATA — Number of points at which the cumulative distribution function is evaluated for interpolation. (Input)
NDATA must be greater than or equal to 4.
Default: NDATA = size (TABLE,1).

LDTABL — Leading dimension of TABLE exactly as specified in the dimension statement in the calling program. (Input)
Default: LDTABL = size (TABLE,1).

FORTRAN 90 Interface

Generic: CALL RNGCT (TABLE, R [, …])

Specific: The specific interface names are S_RNGCT and D_RNGCT.

FORTRAN 77 Interface

Single: CALL RNGCT (NR, NDATA, TABLE, LDTABL, R)

Double: The double precision name is DRNGCT.

Description

Routine RNGCT generates pseudorandom numbers from a continuous distribution using the inverse CDF technique, by interpolation of points of the distribution function given in TABLE, which is set up by routine RNGCS. A strictly monotone increasing distribution function is assumed. The interpolation is by an algorithm attributable to Akima (1970), using piecewise cubics. The use of this technique for generation of random numbers is due to Guerra, Tapia, and Thompson (1976), who give a description of the algorithm and accuracy comparisons between this method and linear interpolation. The relative errors using the Akima interpolation are generally considered very good.

Comments

1. 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.

2. In the interest of efficiency, this routine does only limited error checking. If TABLE is generated by the routine RNGCS, the error checking is sufficient.

Example

In this example, RNGCS is used to set up a table for generation of beta pseudorandom deviates. The CDF for this distribution is computed by the routine BETDF (see Chapter 17, “Probability Distribution Function and Inverses”). The table contains 100 points at which the CDF is evaluated and that are used for interpolation.

 

USE RNGCT_INT

USE UMACH_INT

USE RNGCS_INT

USE RNSET_INT

 

IMPLICIT NONE

INTEGER LDTABL, NR

PARAMETER (LDTABL=100, NR=5)

!

INTEGER I, IOPT, ISEED, NINT, NOUT

REAL CDF, PIN, QIN, R(NR), TABLE(LDTABL,5), X

COMMON /BCOM/ PIN, QIN

EXTERNAL CDF

!

CALL UMACH (2, NOUT)

PIN = 3.0

QIN = 2.0

IOPT = 0

NINT = 100

X = 0.0

! Fill the first column of the table

! with abscissas for interpolation.

DO 10 I=1, NINT

TABLE(I,1) = X

X = X + 0.01

10 CONTINUE

CALL RNGCS (CDF, IOPT, TABLE)

! Initialize seed of random number

! generator.

ISEED = 123457

CALL RNSET (ISEED)

! Now generate the random deviates.

CALL RNGCT (TABLE, R)

WRITE (NOUT,99999) R

99999 FORMAT (' Beta (3,2) random deviates: ', 5F7.4)

END

!

! Beta distribution function

REAL FUNCTION CDF (X)

REAL X

!

REAL BETDF, PIN, QIN

COMMON /BCOM/ PIN, QIN

EXTERNAL BETDF

!

CDF = BETDF(X,PIN,QIN)

RETURN

END

Output

 

*** WARNING ERROR 1 from RNGCS. The values of the CDF in the second

*** column of TABLE did not begin at 0.0 and end at 1.0, but they

*** have been adjusted. Prior to adjustment,

*** TABLE(1,2) = 0.000000E+00 and TABLE(NDATA,2) = 9.994079E-01.

Beta (3,2) random deviates: 0.9208 0.4641 0.7668 0.6536 0.8171