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On the Tractability of Transmuted Type I Generalized Logistic Distribution with Application
International Journal of Theoretical and Applied Mathematics
Volume 5, Issue 2, April 2019, Pages: 31-36
Received: Aug. 9, 2019; Accepted: Aug. 29, 2019; Published: Sep. 16, 2019
Author
Femi Samuel Adeyinka, Department of Mathematics, Obafemi Awolowo University, Ile-Ife, Nigeria
Article Tools Abstract PDF (510KB)
Abstract
Transmutation of baseline distributions has gained popularity in the last decade and many authors have studied the some transmuted distributions such as exponential, Weilbul, gamma, Pareto, normal and many more. This article will focus on the transmutation of type I generalized logistic distribution using quadratic rank transmutation map to develop a transmuted type I generalized logistic distribution. The quadratic rank transmutation map enables the introduction of extra parameter into its parent model to enhance more flexibility in the analysis of data in various disciplines such as biological sciences, actuarial science, finance and insurance. The graphs of the probability density function (pdf) and cumulative distribution function (cdf) of the model for different values of parameters are illustrated respectively. The mathematical properties such as moment generating function, quantile, median and characteristic function of this distribution are discussed. The probability density functions of the minimum and maximum order statistics of the transmuted type I generalized 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 function of the transmuted type I generalized logistic distribution are considered. The parameter estimation is done by the method of maximum likelihood estimation. The flexibility of the model in statistical data analysis and its applicability is demonstrated by using the model to fit relevant data. The study is concluded by demonstrating the performance of transmuted type I generalized logistic distribution over its parent model.
Keywords
Logistic Distribution, Parameter Estimation, Order Statistics, Transmutation
Femi Samuel Adeyinka, On the Tractability of Transmuted Type I Generalized Logistic Distribution with Application, International Journal of Theoretical and Applied Mathematics. Vol. 5, No. 2, 2019, pp. 31-36. doi: 10.11648/j.ijtam.20190502.12
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