The Exponentiated Half-Logistic-Generalized Marshall-Olkin-G Family of Distributions with Properties and Applications
Keywords:
Consistency, flexibility, model parameters, maximum likelihood estimation, simulationsAbstract
In this article, we present a new generalized family of distributions called the Exponentiated Half-Logistic-Generalized Marshall-Olkin-G (EHL-GMO-G) distribution. Some of the useful mathematical and statistical properties for this new family of distributions such as the hazard rate function, quantile function, moments and moment generating functions, Renyi entropy, order statistics and ´stochastic order are derived. The method of maximum likelihood estimation is used for estimating the model parameters. Simulation experiments are conducted to illustrate consistency of the maximum likelihood estimates for model parameters and furthermore we apply one special case of this new family to real life data sets to demonstrate its flexibility in modelling various types of real life data
References
Afify A, Alizadeh M, Zayed M, Ramires T, Louzada F. The Odd Log-Logistic Exponentiated Weibull
Distribution: Regression Modeling, Properties, and Applications. Iran J Sci Technol A. 2027;
(11): 2273-2288.
Afify AZ, Altun E, Alizadeh M, Ozel G, Hamedani GG. The Odd Exponentiated Half-Logistic-G
Family: Properties, Characterizations and Applications. Chil J Stat. 2017; 8(2): 65-91.
Alizadeh M, Cordeiro GM, Nascimento AD, Lima MD, Ortega EM. Odd-Burr generalized family of
distributions with some applications. J Stat Comput Sim.; Springer. 2017; 87(2): 367-389.
Alizadeh M, Tahir MH, Cordeiro GM, Monsoor M, Zubair M, Hamedani GG. The Kumaraswamy
Marshal-Olkin family of distributions. J Egyptian Math Soc. 2015; 23(3): 546-557.
Alzaatreh A, Lee C, Famoye F. A New method for Generating Families of Continuous Distributions.
Metron; Springer. 2013; 71(1): 63-79.
Bourguignon M, Silva RB, Cordeiro GM. The Weibull-G Family of Probability Distributions. J Data
Sci. 2014; 12(1): 53-68.
Burr IW. Cumulative frequency functions. Ann Math. 1942; 13: 215-232.
Chakraborty S, Handique L. The generalized Marshall-Olkin-Kumaraswamy-G family of distributions. J Data Sci. 2017; 15(3): 391-422.
Chen G, Balakhrishnan N. A general purpose approximate goodness-of-fit test. J Qual Technol. 1995;
(2): 154-161.
Cordeiro GM, Alizadeh M, Ortega EM. The exponentiated half-logistic family of distributions: Properties and applications. J Probab Stat. 2014. https://doi.org/10.1155/2014/864396.
Cordeiro GM, Alizadeh M, Tahir MH, Monsoor M, Bourguignon M, Hamedani G. The Beta Odd
log-logistic generalized family of distributions. Hacet J Math Stat. 2016; 45: 1175-1202.
Cordeiro GM, de Castro M. A new family of generalized distributions. J Stat Comput Sim. 2011;
(7): 883-898.
Cordeiro GM, Ortega EM, da Cunha DC. The Exponentiated Generalized Class of Distributions. J
Data Sci. 2013; 11(1): 1-27.
Doostmoradi A, Zadkarami MR, Roshani SA. A New Modified Weibull Distribution and its Applications. J Statist Res Iran. 2014; 11(1): 97-118.
El-Bassiouny AH, Abdo NF, Shahen HS. Exponential lomax distribution. Int J Comput Appl. 2015;
(13): 24-29.
Elbatal I. Exponentiated Modified Weibull Distribution. Stoch Qual Control. 2011; 26(2): 189-200.
Eugene N, Lee C, Famoye F. Beta-normal distribution and its applications. Commun Stat Theory.
; 31(4): 497-512.
Handique L, Chakraborty S. The Marshall-Olkin-Kumarswamy-G family of distributions. arXiv
preprint arXiv:1509.08108. 2015.
Handique L, Chakraborty S. The Beta Generalized Marshall-Olkin-G family of distributions. arXiv
preprint arXiv:1608.05985. 2016.
Marshall A, Olkin I. A new method for adding a parameter to a family of distributions with application
to the exponential and Weibull families. Biometrika. 1997; 84(3): 641-652.
Oluyede B, Moakofi T, Makubate B. A New Gamma Generalized Lindley-Log- logistic Distribution
with Applications. Afrik Stat. 2020; 15: 2451-2479.
Renyi A. On Measures of Entropy and Information. Proceedings of the Fourth Berkeley Symposium ´
on Mathematical Statistics and Probability, Volume 1: Contributions to the Theory of Statistics;
The Regents of the University of California. 1961.
Shaked M, Shanthikumar JG. Stochastic Orders; Springer Science & Business Media. 2007.
Shannon CE. Prediction and entropy of printed English. Bell Syst Tech J. 1951; 30(1): 50-64.
Shaw WT, Buckley RC. The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map. arXiv preprint
arXiv:0901.0434. 2009.
Sindhu T, Shafiq A, Al-Mdallal Q. Exponentiated transformation of Gumbel Type-II distribution for
modeling COVID-19 data. Alex Eng J. 2020; 60(10); doi:10.1016/j.aej.2020.09.060.
Tahir MH, Cordeiro GM, Mansoor M, Zubair M. The Weibull-Lomax Distribution: Properties and
Applications. Hacettepe J Math Stat. 2015; 44(2): 461-480.
Torabi H, Montazeri NH. The logistic-uniform distribution and its applications. Commun Stat Simulat. 2014; 43(10): 2551-2569.
Yousof HM, Afify AZ, Nadarajah S, Hamedani G, Aryal GR. The Marshall-Olkin generalized-G
family of distributions with Applications. Statistica. 2018; 78(3): 273-295.
Zografos K, Balakhrishnan N. On Families of Beta and Generalized Gamma generated Distribution
and Associated Inference. Stat Methodol. 2009; 6: 344-362.
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
