On approximating the distribution of quadratic forms in uniform and beta order statistics

摘要

This paper provides a moment-based approximation to the distribution of a quadratic forms in uniform random variables and in order statistics from a uniform population. Certain goodness-of-fit statistics can be expressed in terms of the latter. In particular, it is shown that the proposed methodology yields more accurate percentiles than a previously used approximation in connection with a criterion that is expressible as a quadratic form in order statistics from a uniform distribution. The more general case of quadratic forms in beta random variables is also discussed. The density approximants are expressed as the product of a beta distributed base density function and a polynomial adjustment. Several illustrative examples are provided.