Journal of Statistical Theory and Applications

Volume 20, Issue 2, June 2021, Pages 228 - 241

The Odd Log-Logistic Burr-X Family of Distributions: Properties and Applications

Authors
Hamid Karamikabir1, Mahmoud Afshari1, *, Morad Alizadeh1, Haitham M. Yousof2
1 Department of Statistics, Faculty of Intelligent Systems Engineering and Data Science, Persian Gulf University, Bushehr, 7516913798, Iran
2 Department of Statistics, Mathematics and Insurance, Benha University, Benha, Egypt
*Corresponding author. Email: afshar@pgu.ac.ir
Corresponding Author
Mahmoud Afshari
Received 1 September 2020, Accepted 15 June 2021, Available Online 15 June 2021.
DOI
https://doi.org/10.2991/jsta.d.210609.001How to use a DOI?
Keywords
Odd log-logistic-G family, Burr-X family, Maximum likelihood method, Least square method, Weighted least square method, Moments
Abstract

In this paper, a new class of distributions called the odd log-logistic Burr-X family with two extra positive parameters is introduced and studied. The new generator extends the odd log-logistic and Burr X distributions among several other well-known distributions. We provide some mathematical properties of the new family including asymptotics, moments, moment-generating function and incomplete moments. Different methods have been used to estimate its parameters such as maximum likelihood, least squares, weighted least squares, Cramer–von-Mises, Anderson–Darling and right-tailed Anderson–Darling methods. We evaluate the performance of the maximum likelihood estimators in terms of biases and mean squared errors by means of a simulation study. Finally, the usefulness of the family is illustrated by means of three real data sets. The new models provide consistently better fits than other competitive models for these data sets. The new family is suitable for fitting different real data sets, the odd log-logistic Burr-X Normal model is used for modeling bimodal and skewed data sets and can be sued as an alternative to the gamma-normal, beta-normal, McDonald-normal, Marshall-Olkin-normal, Kumaraswamy-normal, Zografos-Balakrishnan and Log-normal distributions.

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
228 - 241
Publication Date
2021/06/15
ISSN (Online)
2214-1766
ISSN (Print)
1538-7887
DOI
https://doi.org/10.2991/jsta.d.210609.001How 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  - Hamid Karamikabir
AU  - Mahmoud Afshari
AU  - Morad Alizadeh
AU  - Haitham M. Yousof
PY  - 2021
DA  - 2021/06/15
TI  - The Odd Log-Logistic Burr-X Family of Distributions: Properties and Applications
JO  - Journal of Statistical Theory and Applications
SP  - 228
EP  - 241
VL  - 20
IS  - 2
SN  - 2214-1766
UR  - https://doi.org/10.2991/jsta.d.210609.001
DO  - https://doi.org/10.2991/jsta.d.210609.001
ID  - Karamikabir2021
ER  -