Abstract
In this article, we address the problem of computing the distribution functions that can be
expressed as discrete mixtures of continuous distributions. Examples include noncentral chisquare,
noncentral beta, noncentral F, noncentral t, and the distribution of squared sample multiple
correlation. We illustrate the need for improved algorithms by pointing out situations where
existing algorithms fail to compute meaningful values of the cumulative distribution functions
(cdf) under study. To address this problem we recommend an approach that can be easily
incorporated to improve the existing algorithms. For the distributions of the squared sample
multiple correlation coe+cient, noncentral t, and noncentral chisquare, we apply the approach
and give a detailed explanation of computing the cdf values. We present results of comparison
studies carried out to validate the calculated values and computational times of our suggested
approach. Finally, we give the algorithms for computing the distributions of the squared sample
multiple correlation coe+cient, noncentral t, and noncentral chisquare so that they can be coded
in any desired computer language.
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