Volume 5, Issue 2, June 2019, Page: 32-37
On Transmuted Four Parameters Generalized Log-Logistic Distribution
Femi Samuel Adeyinka, Department of Mathematics, Obafemi Awolowo University, Ile-Ife, Nigeria
Akintayo Kehinde Olapade, Department of Mathematics, Obafemi Awolowo University, Ile-Ife, Nigeria
Received: May 5, 2019;       Accepted: Jun. 5, 2019;       Published: Jul. 16, 2019
DOI: 10.11648/j.ijsd.20190502.12      View  129      Downloads  28
Abstract
In this article we transmute the four parameters generalized log-logistic distribution using quadratic rank transmutation map to develop a transmuted four parameters generalized log-logistic distribution. The quadratic rank transmutation map helps to introduce extra parameter into the baseline distribution to enhance more flexibility in the analysis of data in various disciplines such as reliability analysis in engineering, survival analysis, medicine, biological sciences, actuarial science, finance and insurance. The mathematical properties such as moments, quantile, mean, median, variance, skewness and kurtosis of this distribution are discussed. The reliability and hazard functions of the four parameters generalized log-logistic distribution are obtained. The probability density functions of the minimum and maximum order statistics of the four parameters generalized log-logistic distribution are established and the relationships between the probability density functions of the minimum and maximum order statistics of the parent model and the probability density functions of the four parameters generalized log-logistic distribution are considered. The parameter estimation is done by the maximum likelihood method. The flexibility of the model in statistical data analysis and its applicability is demonstrated by using it to fit relevant data. The study is concluded by demonstrating that the four parameters generalized log-logistic distribution has a better goodness of fit than its parent model. We hope this model will serve as an alternative to the existing ones in fitting positive real data.
Keywords
Log-Logistic Distribution, Reliability Function, Hazard Rate Function, Parameter Estimation, Order Statistics, Transmutation
To cite this article
Femi Samuel Adeyinka, Akintayo Kehinde Olapade, On Transmuted Four Parameters Generalized Log-Logistic Distribution, International Journal of Statistical Distributions and Applications. Vol. 5, No. 2, 2019, pp. 32-37. doi: 10.11648/j.ijsd.20190502.12
Copyright
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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