A Versatile Probabilistic Model based on Yun-G Family of Distributions and its Applications in Engineering Sector

Yun-G family of distributions and its application

In this paper, we introduce a new generalization of univariate and bivariate modified discrete Weibull distribution. Various properties of the univariate generalized modified discrete Weibull distribution, such as survival function, probability mass function, hazard rate function, probability generating function, and moment generating function, are derived. The joint distribution function, joint probability mass function, marginal distributions, moment generating function, and conditional distribution of the proposed bivariate distribution are derived. Parameters of the distributions are estimated using maximum likelihood estimation. The use of these distributions is illustrated using real-life datasets.

The present paper discusses a versatile three -parameter distribution from the Yun-G family. The important statistical properties like moments, stochastic ordering, and entropy are studied in this paper. Two characterizations of the distribution are obtained using the hazard rate function and truncated moments. The statistical inference of the distribution is studied by executing five different methods of parameter estimation, such as maximum likelihood estimation, ordinary least square method, weighted least square method, Cramer-von Mises method, and Anderson–Darling method. To study the fitting and applicability of the proposed distribution, two real life data sets from the engineering sector were analyzed and the proposed distribution is found to be more appropriate than the other competitive distributions. A comprehensive simulation study is also conducted and it showed the accuracy and consistency of the estimation techniques.