Distribution of a Sum of Weighted Noncentral Chi-Square Variables

- Journal title : Communications for Statistical Applications and Methods
- Volume 13, Issue 2, 2006, pp.429-440
- Publisher : The Korean Statistical Society
- DOI : 10.5351/CKSS.2006.13.2.429

Title & Authors

Distribution of a Sum of Weighted Noncentral Chi-Square Variables

Heo, Sun-Yeong; Chang, Duk-Joon;

Heo, Sun-Yeong; Chang, Duk-Joon;

Abstract

In statistical computing, it is often for researchers to need the distribution of a weighted sum of noncentral chi-square variables. In this case, it is very limited to know its exact distribution. There are many works to contribute to this topic, e.g. Imhof (1961) and Solomon-Stephens (1977). Imhof's method gives good approximation to the true distribution, but it is not easy to apply even though we consider the development of computer technology Solomon-Stephens's three moment chi-square approximation is relatively easy and accurate to apply. However, they skipped many details, and their simulation is limited to a weighed sum of central chi-square random variables. This paper gives details on Solomon-Stephens's method. We also extend their simulation to the weighted sum of non-central chi-square distribution. We evaluated approximated powers for homogeneous test and compared them with the true powers. Solomon-Stephens's method shows very good approximation for the case.

Keywords

Newton-Raphson iteration;Wald test;Homogeneous test;

Language

Korean

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