Generates pseudorandom numbers from a multivariate distribution determined from a given sample.

The type double function is imsls_d_random_mvar_from_data.

n_random × ndim matrix containing the random multivariate vectors in its rows. To release this space, use imsls_free.

Given a sample of size n (= nsamp) of observations of a k-variate random variable, imsls_f_random_mvar_from_data generates a pseudorandom sample with approximately the same moments as the given sample. The sample obtained is essentially the same as if sampling from a Gaussian kernel estimate of the sample density. (See Thompson 1989.) Function imsls_f_random_mvar_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_random such simulated variates are generated and stored in the rows of the result.

In this example, imsls_f_random_mvar_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 function imsls_f_data_sets, Chapter 15, Utilities.)