The Kumaraswamy Marshall-Olkin Log-Logistic Distribution with Application

In this paper, we define and study a new lifetime model called the Kumaraswamy Marshall-Olkin log-logistic distribution. The new model has the advantage of being capable of modeling various shapes of aging and failure criteria. The new model contains some well-known distributions as special cases such as the Marshall-Olkin loglogistic, log-logistic, lomax, Pareto type II and Burr XII distributions. Some of its mathematical properties including explicit expressions for the quantile and generating functions, ordinary moments, skewness, kurtosis are derived. The maximum likelihood estimators of the unknown parameters are obtained. The importance and flexibility of the new model is proved empirically using a real data set.

[1]  Saralees Nadarajah,et al.  General results for the Kumaraswamy-G distribution , 2012 .

[2]  Gauss M. Cordeiro,et al.  The Weibull-G Family of Probability Distributions , 2014, Journal of Data Science.

[3]  F. Famoye,et al.  The beta-Pareto distribution , 2008 .

[4]  Richard L. Smith,et al.  A Comparison of Maximum Likelihood and Bayesian Estimators for the Three‐Parameter Weibull Distribution , 1987 .

[5]  Zohdy M. Nofal,et al.  The Weibull Fréchet distribution and its applications , 2016 .

[6]  I. Olkin,et al.  A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families , 1997 .

[7]  Zohdy M. Nofal,et al.  The Kumaraswamy Transmuted-G Family of Distributions: Properties and Applications , 2021 .

[8]  Gauss M. Cordeiro,et al.  A new family of generalized distributions , 2011 .

[9]  Natalie Verónika Rondinel Mendoza,et al.  The exponentiated-log-logistic geometric distribution: Dual activation , 2016 .

[10]  Tsuyoshi Murata,et al.  {m , 1934, ACML.

[11]  Wolegang Glanzel,et al.  Some consequences of a characterization theorem based on truncated moments , 1990 .

[12]  M. H. Tahir,et al.  The Kumaraswamy Marshal-Olkin family of distributions , 2015 .

[13]  Wolfgang Glänzel,et al.  A Characterization Theorem Based on Truncated Moments and its Application to Some Distribution Families , 1987 .

[14]  F. Famoye,et al.  BETA-NORMAL DISTRIBUTION AND ITS APPLICATIONS , 2002 .

[15]  Gauss M. Cordeiro,et al.  The Kumaraswamy-Log-Logistic Distribution , 2012 .

[16]  Hamzeh Torabi,et al.  The Logistic-Uniform Distribution and Its Applications , 2014, Commun. Stat. Simul. Comput..

[17]  On Generalized Gamma Convolution Distributions , 2013 .

[18]  Gauss M. Cordeiro,et al.  The Lomax generator of distributions: Properties, minification process and regression model , 2014, Appl. Math. Comput..

[19]  S. Nadarajah,et al.  The beta transmuted-H family for lifetime data , 2017 .

[20]  A. Rényi.  On Measures of Entropy and Information , 1961 .

[21]  Wenhao Gui.  Marshall-Olkin extended log-logistic distribution and its application in minification processes , 2013 .

[22]  Claude E. Shannon,et al.  Prediction and Entropy of Printed English , 1951 .

[23]  M. H. Tahir,et al.  McDonald log-logistic distribution with an application to breast cancer data , 2014, J. Stat. Theory Appl..

[24]  Zohdy M. Nofal,et al.  The generalized transmuted-G family of distributions , 2017 .

[25]  Francisco Louzada,et al.  The Transmuted Log-Logistic Distribution: Modeling, Inference, and an Application to a Polled Tabapua Race Time up to First Calving Data , 2015 .

[26]  Ayman Alzaatreh,et al.  A new method for generating families of continuous distributions , 2013 .

[27]  Artur J. Lemonte.  The beta log-logistic distribution , 2014 .