Journal of Statistical Theory and Applications

Volume 20, Issue 2, June 2021, Pages 219 - 227

An Alternative Measures of Moments Skewness Kurtosis and JB Test of Normality

Authors
Md. Siraj-Ud-Doulah*
Department of Statistics, Begum Rokeya University, Rangpur, 5400, Bangladesh
*Corresponding author. Email: sdoulah_brur@yahoo.com
Corresponding Author
Md. Siraj-Ud-Doulah
Received 30 October 2018, Accepted 31 December 2020, Available Online 31 May 2021.
DOI
https://doi.org/10.2991/jsta.d.210525.002How to use a DOI?
Keywords
Robust moments, Robust skewness, Robust Kurtosis, Robust test of normality
Abstract

If we know the statistics of central tendency and dispersion, we still cannot nature a complete design about the distribution. About these measures we should know more information's of skewness and kurtosis, which are enables us to have a design the distribution. However, there is evidence that they may response poorly in the presence of non-normality or when outliers arise in data. We examine the performances of popular and frequently used measures of skewness β1, kurtosis β2 and Jarque–Bera test of normality that they may not perform and we anticipates in the existence of non-normality or outliers. In this paper, firstly, we develop robust measures of moments and we formulate a new statistics of skewness and kurtosis which we name robust skewness ϕ1 and robust kurtosis ϕ2. Again, in this paper, we modify Jarque–Bera test of normality, which we label Robust Jarque–Bera (RJB). These measures should be fairly robust. The effectiveness of the proposed measures is investigated by simulation approach. The results demonstrate that the newly proposed skewness ϕ1, kurtosis ϕ2 and RJB test outperform the skewness, kurtosis and Jarque–Bera test of normality when a small percentage of outliers are present or absent in the data.

Copyright
© 2021 The Authors. Published by Atlantis Press B.V.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Statistical Theory and Applications
Volume-Issue
20 - 2
Pages
219 - 227
Publication Date
2021/05/31
ISSN (Online)
2214-1766
ISSN (Print)
1538-7887
DOI
https://doi.org/10.2991/jsta.d.210525.002How to use a DOI?
Copyright
© 2021 The Authors. Published by Atlantis Press B.V.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Md. Siraj-Ud-Doulah
PY  - 2021
DA  - 2021/05/31
TI  - An Alternative Measures of Moments Skewness Kurtosis and JB Test of Normality
JO  - Journal of Statistical Theory and Applications
SP  - 219
EP  - 227
VL  - 20
IS  - 2
SN  - 2214-1766
UR  - https://doi.org/10.2991/jsta.d.210525.002
DO  - https://doi.org/10.2991/jsta.d.210525.002
ID  - Siraj-Ud-Doulah2021
ER  -