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

Serge Provost () and A. Mohsenipour ()

METRON, 2013, vol. 71, issue 2, 123-138

Abstract: 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. Copyright Sapienza Università di Roma 2013

Keywords: Quadratic forms; Uniform random variables; Order statistics; Beta random variables; Moments; Goodness-of-fit statistics (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s40300-013-0014-z

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