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 E12E ≥E12N and E21E ≥E21N 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.
| Published in | American Journal of Theoretical and Applied Statistics (Volume 8, Issue 6) |
| DOI | 10.11648/j.ajtas.20190806.12 |
| Page(s) | 203-213 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2024. Published by Science Publishing Group |
Errors of Misclassification, Edgeworth Series Distribution, Skewness Factor, Classificatory Rule, Optimum Probability of Misclassification
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APA Style
Awogbemi Clement Adeyeye, Onyeagu Sidney Iheanyi. (2019). Errors of Misclassification Associated with Edgeworth Series Distribution (ESD). American Journal of Theoretical and Applied Statistics, 8(6), 203-213. https://doi.org/10.11648/j.ajtas.20190806.12
ACS Style
Awogbemi Clement Adeyeye; Onyeagu Sidney Iheanyi. Errors of Misclassification Associated with Edgeworth Series Distribution (ESD). Am. J. Theor. Appl. Stat. 2019, 8(6), 203-213. doi: 10.11648/j.ajtas.20190806.12
AMA Style
Awogbemi Clement Adeyeye, Onyeagu Sidney Iheanyi. Errors of Misclassification Associated with Edgeworth Series Distribution (ESD). Am J Theor Appl Stat. 2019;8(6):203-213. doi: 10.11648/j.ajtas.20190806.12
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Download@article{10.11648/j.ajtas.20190806.12,
author = {Awogbemi Clement Adeyeye and Onyeagu Sidney Iheanyi},
title = {Errors of Misclassification Associated with Edgeworth Series Distribution (ESD)},
journal = {American Journal of Theoretical and Applied Statistics},
volume = {8},
number = {6},
pages = {203-213},
doi = {10.11648/j.ajtas.20190806.12},
url = {https://doi.org/10.11648/j.ajtas.20190806.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20190806.12},
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 E12E ≥E12N and E21E ≥E21N 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.},
year = {2019}
}
TY - JOUR T1 - Errors of Misclassification Associated with Edgeworth Series Distribution (ESD) AU - Awogbemi Clement Adeyeye AU - Onyeagu Sidney Iheanyi Y1 - 2019/11/08 PY - 2019 N1 - https://doi.org/10.11648/j.ajtas.20190806.12 DO - 10.11648/j.ajtas.20190806.12 T2 - American Journal of Theoretical and Applied Statistics JF - American Journal of Theoretical and Applied Statistics JO - American Journal of Theoretical and Applied Statistics SP - 203 EP - 213 PB - Science Publishing Group SN - 2326-9006 UR - https://doi.org/10.11648/j.ajtas.20190806.12 AB - 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 E12E ≥E12N and E21E ≥E21N 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. VL - 8 IS - 6 ER -
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