Errors of Misclassification Associated with Edgeworth Series Distribution (ESD)
American Journal of Theoretical and Applied Statistics
Volume 8, Issue 6, November 2019, Pages: 203-213
Received: Mar. 2, 2018; Accepted: Mar. 30, 2018; Published: Nov. 8, 2019
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Authors
Awogbemi Clement Adeyeye, Statistics Department, Nnamdi Azikiwe University, Awka, Nigeria
Onyeagu Sidney Iheanyi, Statistics Department, Nnamdi Azikiwe University, Awka, Nigeria
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Abstract
This study investigates the errors of misclassification associated with Edgeworth Series Distribution (ESD) with a view to assessing the effects of sampling from non-normality. The effects of applying a normal classificatory rule when it is actually a persistent non-normal distribution were examined. These were achieved by comparing the errors of misclassification for ESD with ND using small sample sizes at every level of skewness factor. The simulation procedure for the experiment of the study was implemented using numerical inverse interpolation method in R program to generate a uniformly distributed random variable N. A configuration size of 1000 was obtained for the two training samples drawn at every level of skewness factor (λ3), in the range (0.00625, 0.4). This was repeated for different small sample sizes by comparing errors of misclassification of ESD with ND. The simulation results showed that the optimum probabilities of misclassification by ESD: (E12E) decreases and (E12E) increases, as the skewness factor (λ3) increases. The optimum total probability of misclassification is stable as λ3 also increases. The probability of misclassification E12EE12N and E21EE21N at every level of λ3. Thus, the total probabilities of misclassification are not greatly affected by the skewness factor. This asserts that the normal classification procedure is robust against departure from normality.
Keywords
Errors of Misclassification, Edgeworth Series Distribution, Skewness Factor, Classificatory Rule, Optimum Probability of Misclassification
To cite this article
Awogbemi Clement Adeyeye, Onyeagu Sidney Iheanyi, Errors of Misclassification Associated with Edgeworth Series Distribution (ESD), American Journal of Theoretical and Applied Statistics. Vol. 8, No. 6, 2019, pp. 203-213. doi: 10.11648/j.ajtas.20190806.12
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Copyright © 2019 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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