Statistical inference for Pr(Y
Technometrics
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Editorial: Advances in Mixture Models
Computational Statistics & Data Analysis
On the computation of the noncentral F and noncentral beta distribution
Statistics and Computing
Implementing Bayesian predictive procedures: The K-prime and K-square distributions
Computational Statistics & Data Analysis
Computing the noncentral gamma distribution, its inverse and the noncentrality parameter
Computational Statistics
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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 coefficient, 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 coefficient, noncentral t, and noncentral chisquare so that they can be coded in any desired computer language.