IMSL_RAND_FROM

IMSL_RAND_FROM_DATA

The IMSL_RAND_FROM_DATA function generates pseudorandom numbers from a multivariate distribution determined from a given sample.

This routine requires an IDL Advanced Math and Stats license. For more information, contact your sales or technical support representative.

Given a sample of size nsamp of observations of a k-variate random variable, IMSL_RAND_FROM_DATA generates a pseudorandom sample with approximately the same moments as the given sample. The sample obtained is the same as if sampling from a Gaussian kernel estimate of the sample density. (See Thompson 1989.) Routine IMSL_RAND_FROM_DATA uses methods described by Taylor and Thompson (1986).

Assume that the (vector-valued) observations x_i are in the rows of x. An observation, x_j, is chosen randomly; its nearest m (= nn) neighbors:

are determined; and the mean:

x_j

of those nearest neighbors is calculated. Next, a random sample u₁, u₂, ..., u_m is

generated from a uniform distribution with lower bound:

and upper bound:

The random variate delivered is:

The process is then repeated until n such simulated variates are generated and stored in the rows of the result.

Example

For additional information on using XYZ Routine, see Additional Examples.

In this example, IMSL_RAND_FROM_DATA is used to generate 5 pseudorandom vectors of length 4 using the initial and final systolic pressure and the initial and final diastolic pressure from Data Set A in Afifi and Azen (1979) as the fixed sample from the population to be modeled. (Values of these four variables are in the seventh, tenth, twenty-first, and twenty-fourth columns of data set number nine in routine IMSL_STATDATA.)

IMSL_RANDOMOPT, Set = 123457

r = IMSL_STATDATA(9)

x = FLTARR(113, 4)

x(*, 0) = r(*,6)

x(*, 1) = r(*,9)

x(*, 2) = r(*,20)

x(*, 3) = r(*,23)

r = IMSL_RAND_FROM_DATA(5, x, 5)

PM, r

162.767 90.5057 153.717 104.877

153.353 78.3180 176.664 85.2155

93.6958 48.1675 153.549 71.3688

101.751 54.1855 113.121 56.2916

91.7403 58.7684 48.4368 28.0994

Syntax

Result = IMSL_RAND_FROM_DATA(N_random, X, Nn [, /DOUBLE])

Return Value

N x ndim matrix containing the random multivariate vectors in its rows.

Arguments

N_Random

Number of random multivariate vectors to generate.

Nn

Number of nearest neighbors of the randomly selected point in x that are used to form the output point in the result.

X

Two dimensional array of size nsamp by ndim containing the given sample.

Keywords

DOUBLE (optional)

If present and nonzero, double precision is used.

Version History

6.4	Introduced

Module	Math&Stats

Version	9.0