Abstract
Abstract Some justifications for the Roy-Tiku (1962) approximation to the distributions of sample variances by Laguerre polynomial series are provided. It is shown that if one approximates any nonnegative continuous random variable by a finite series of Laguerre polynomials up to the kth degree, then the first k moments of the approximated distribution are equal to the first k moments of the random variable. We also derive an alternative Laguerre series approximation, including the Box (1953) approximation as a special case.
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