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

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 xi are in the rows of x. An observation, xj, 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, ..., um 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.

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