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Volume 4, Issue 1, June 2020, Page: 1-9
Asymptotic Distribution of Probabilities of Misclassification for Edgeworth Series Distribution (ESD)
Awogbemi Clement Adeyeye, Statistics Department, National Mathematical Centre, Abuja, Nigeria
Received: Oct. 16, 2019;       Accepted: Nov. 12, 2019;       Published: May 28, 2020
DOI: 10.11648/j.engmath.20200401.11      View  393      Downloads  70
Abstract
The exact distribution of the test statistics in multivariate case is quite complicated in many situations, even when the underlying distribution is multivariate normal. This is due to the complex nature of the expression and therefore, there is a need to derive the asymptotic expression for the distribution. In this study, the asymptotic distribution of errors of misclassification for Edgeworth Series is derived by using Taylor’s expansion. The error of misclassification for the conditional probability of misclassification was expanded around the means emanating from populations one and two using approximated mean and variance of the errors of misclassification. The distribution of error of misclassification of the conditional probability of misclassification for ESD is approximately normal with mean zero and variance one.
Keywords
Asymptotic Distribution, Probability of Misclassification, Edgeworth Series Distribution, Approximate Mean, Approximate Variance
To cite this article
Awogbemi Clement Adeyeye, Asymptotic Distribution of Probabilities of Misclassification for Edgeworth Series Distribution (ESD), Engineering Mathematics. Vol. 4, No. 1, 2020, pp. 1-9. doi: 10.11648/j.engmath.20200401.11
Copyright
Copyright © 2020 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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