| Abstract |
Summary
Statistical distributions have a great importance in the scientific research which are commonly applied to describe the real phenomena. Thus, several statistical distributions have been extensively used in data analysis in several areas of research such as medical, engineering, reliability, etc. However, in many situations, the classical distributions are not appropriate for describing the data and the real phenomena, so many statisticians have introduced new families of distributions by adding a shape parameter(s) to these distributions to deal with this problem. Thus, in this study, three distributions named “Beta Exponentiated Kumaraswamy distribution”, “Beta Exponentiated Generalized Extended Pareto distribution”, and “Beta Exponentiated Inverse Rayleigh distribution” are presented. Some statistical properties and Maximum Likelihood estimation are obtained. Bayesian estimation is studied for each distribution for 3 types of priors that included informative and non-informative prior. Applied studies for Beta Generalized Inverted Kumaraswamy distribution, Beta Exponentiated Generalized Extended Pareto distribution, and Beta Exponentiated Inverse Rayleigh distribution are provided using Mathematica Package 12. we used the Monte Carlo simulation to study the behavior of the parameter’s estimator in different samples size for different priors, and we used the R language to conduct the Monte Carlo simulation study.
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| Keywords |
hazard rate function, moment generating function, Renyi entropy, beta
distribution, beta exponentiated inverse Rayleigh, beta exponentiated Kumaraswamy, Beta Exponentiated Generalized Extended Pareto maximum likelihood, and Bayesian estimation. |
