On Transmuted Type II Generalized Logistic Distribution with Application
American Journal of Applied Mathematics
Volume 7, Issue 6, December 2019, Pages: 177-182
Received: Nov. 13, 2019; Accepted: Dec. 17, 2019; Published: Dec. 31, 2019
Views 35      Downloads 41
Femi Samuel Adeyinka, Department of Mathematics, Obafemi Awolowo University, Ile-Ife, Nigeria
Article Tools
Follow on us
Introducing extra parameters into the baseline distribution has been a huge breakthrough in research as this enhances more flexibility of the existing models. One of the recent methods is the use of transmutation map which has attracted the interest of many researchers in the last decade. This article investigates the flexibility of transmuted type II generalized logistic distribution. The well-known type II generalized logistic distribution is transmuted using quadratic rank transmutation map to develop a transmuted type II generalized logistic distribution. The map enables the introduction of additional parameter into its parent model to make it more flexible in the analysis of data in various disciplines such as biological sciences, actuarial science, finance and insurance. Some statistical properties of the model are considered and these properties include the moment, quantiles and functions of minimum and maximum order statistics. The estimation issue of the subject model is addressed using method of maximum likelihood estimation. The model is applied to real life data to demonstrate its performance and the comparison of the result of the subject model with its parent model was done using Akaike Information criterion (AIC), Corrected Akaike Information criterion (AICC) and Bayesian Information criterion (BIC) respectively. It is believed that the results from this research work will be of immense contributions in this field and other related disciplines in modelling real data.
Generalized Logistic Distribution, Maximum Likelihood, Order Statistics, Parameter Estimation, Transmutatio
To cite this article
Femi Samuel Adeyinka, On Transmuted Type II Generalized Logistic Distribution with Application, American Journal of Applied Mathematics. Special Issue: On Transmuted Family of Distributions with Applications. Vol. 7, No. 6, 2019, pp. 177-182. doi: 10.11648/j.ajam.20190706.15
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.
Balakrishnan 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.
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.
Adeyinka, F. S. (2019). On the Tractability of Transmuted Type I Generalized Logistic Distribution with Application. International Journal of Theoretical and Applied Mathematics. 5 (2): 31-36.
AL-Kadim, K. A. and Mohammed, M. H. (2017). The cubic transmuted Weibull distribution. Journal of University of Babylon, 3: 862876.
Granzotto, 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.
David, H. A. (1970) Order Statistics. New York: Wiley Inter-science series.
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.
Gupta, R. D., Kundu, D. (2010). Generalized Logistic Distributions. Journal of Applied Statistical Science.18, 51-66.
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
Tel: (001)347-983-5186