IDL Analyst Reference Guide: Random Number Generation

IMSL_RAND_FROM_DATA

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

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

If present and nonzero, double precision is used.

Discussion

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:

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

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, see Math and Statistics Utilities of this manual).

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