RAND_GEN_CONT Function (PV-WAVE Advantage)

IMSL Statistics Reference Guide > Random Number Generation > RAND_GEN_CONT Function (PV-WAVE Advantage)

Generates pseudorandom numbers from a general continuous distribution.

Usage

result = RAND_GEN_CONT(n, table)

Input Parameters

n—Number of random numbers to generate.

table—A two-dimensional array setup using CONT_TABLE to be used for interpolation of the cumulative distribution function. 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.

Returned Value

result—An array of length n containing the random deviates.

Input Keywords

Double—If present and nonzero, double precision is used.

Discussion

Routine RAND_GEN_CONT 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 CONT_TABLE Procedure (PV-WAVE Advantage). 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.

Example

In this example, RAND_GEN_CONT Function (PV-WAVE Advantage) is used to set up a table for generation of beta pseudorandom deviates. The CDF for this distribution is computed by the routine BETACDF. The table contains 100 points at which the CDF is evaluated and that are used for interpolation. Notice that two warnings are issued during the computations for this example.

FUNCTION cdf, x

   RETURN, BETACDF(x, 3., 2.)

END

iopt = 0

ndata = 100;

table = FLTARR(100, 5)

x = 0.0;

table(*,0) = FINDGEN(100)/100.

CONT_TABLE, 'cdf', iopt, ndata, table

RANDOMOPT, Set = 123457

r = RAND_GEN_CONT(5, table)

; % BETACDF: Note: STAT_ZERO_AT_X

; Since 'X' = 0.000000e+00 is less than or equal to zero,

; the distribution function is zero at 'x'.

; % CONT_TABLE: Warning: STAT_SECOND_COL_TABLE3

; 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(0, 1) = 0.000000e+00 and

; table(ndata-1, 1)= 9.994079e-01.

PM, r

; PV-WAVE prints the following:

; 0.92079391

; 0.46412855

; 0.76678398

; 0.65357975

; 0.81706959

Version 2017.0