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
Views 592 Downloads 120
Femi Samuel Adeyinka, Department of Mathematics, Obafemi Awolowo University, Ile-Ife, Nigeria
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.
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.
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.
Balakrishan N. and Leung M. Y. (1988). Order Statistics from the Type I Generalized logistic distribution. Communications in Statistics simulation and computation. Vol 17 (1) 25-50.
Shaw, W. T, and Buckley, I. R. (2009). Alchemy of Probability Distributions: Beyond Gram-Charlier and Cornish -Fisher Expansions, and Skewed- kurtotic Normal Distribution from a Rank Transmutation Map. arxivpreprint arxiv: 0901.0434.
Aryal, G. R, and Tsokos, C. P. (2009). On the transmuted extreme value distribution with application. Nonlinear Analysis: Theory, Methods and Application.71 (12), el401-el407.
Aryal, G. R, and Tsokos, C. P. (2011). Transmuted Weilbull distribution: A generalization of Weilbull probability distribution. European Journal of Pure and Applied Mathematics. 4 (2), 89-102.
Aryal, G. R. (2013). Transmuted log-logistic distribution. Journal of Statistics Applications and probability. 2 (1), 11-20.
Merovci, F., Alizadeh, M., and Hamedani, G. (2016). Another Generalized Transmuted Family of Distributions: Properties and Applications. Austrian Journal of Statistics. 45, 71-93.
Merovci, F., Elbatal, I. (2014). Transmuted Lindley-geometric Distribution and its Applications. Journal of Statistics Applications and Probability. 3 (1), 77-91.
Merovci, F. (2014). Transmuted Generalized Rayleigh Distribution. Journal of Statistics Applications and Probability. 3 (1), 9-20.
Merovci, F., Puka, L. (2014). Transmuted Pareto Distribution. Probstat.7, 1-11.
Merovci, F. (2013). Transmuted Lindley Distribution. International Journal of open Problems in Computer Science and Mathematics. 6 (2), 63-72.
AL-Kadim, K. A. and Mohammed, M. H. (2017). The cubic transmuted Weibull distribution. Journal of University of Babylon, 3: 862876.
Granzoto, D. C. T., Louzada, F., and Balakrishnan, N. (2017). Cubic rank transmuted distributions: Inferential issues and applications. Journal of statistical Computation and Simulation.
Rahman M. M, Al-Zahrani B, Shahbaz M. Q (2018). A general transmuted family of distributions. Pak J Stat Oper Res 14: 451-469.
Adeyinka F. S, and Olapade, A. K. (2019). On Transmuted Four Parameters Generalized Log-Logistic Distribution. International Journal of Statistical Distributions and Applications. 5 (2): 32-37.
Adeyinka F. S and Olapade A. K. (2019). A Study on Transmuted Half Logistic Distribution: Properties and Application. International Journal of Statistical Distributions and Applications. 5 (3): 54-59.
Adeyinka F. S, and Olapade, A. K. (2019). On the Flexibility of a Transmuted Type I Generalized Half-Logistic Distribution with Application. Engineering Mathematics. 3 (1): 13-18.
Adeyinka F. S. (2019). On the Performance of Transmuted Logistic Distribution: Statistical Properties and Application. Budapest International Research in Exact Sciences (BirEx) Journal. 1 (3): 34-42.
David, H. A. (1970) Order Statistics. New York: Wiley Inter-science series.
Gupta, R. D., Kundu, D. (2010). Generalized Logistic Distributions. Journal of Applied Statistical Science.18, 51-66.
Badar, M. G. and Priest, A. M. (1982), “Statistical aspects of ﬁber and bundle strength in hybrid composites”, Progress in Science and Engineering Composites, Hayashi, T., Kawata, K. and Umekawa, S. (eds.), ICCM-IV, Tokyo, 1129-1136.