A new chi-square approximation to the distribution of non-negative definite quadratic forms in non-central normal variables

Huan Liu, Yongqiang Tang and Hao Helen Zhang

Computational Statistics & Data Analysis, 2009, vol. 53, issue 4, 853-856

Abstract: This note proposes a new chi-square approximation to the distribution of non-negative definite quadratic forms in non-central normal variables. The unknown parameters are determined by the first four cumulants of the quadratic forms. The proposed method is compared with Pearson's three-moment central [chi]2 approximation approach, by means of numerical examples. Our method yields a better approximation to the distribution of the non-central quadratic forms than Pearson's method, particularly in the upper tail of the quadratic form, the tail most often needed in practical work.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:53:y:2009:i:4:p:853-856

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