Study on Zografos-Balakrishnan G-Family of Distributions

Abstract

For any continuous baseline G distribution, Zografos and Balakrishnan (2009) proposed generalized gamma generated G-family of Distributions with an extra positive parameter. Nadarajah and Cordiero (2015) proposed various mathematical properties of such distributions. Lee and Famaye (2014) proposed the T-X family of distributions. As a part of these two families we propose two new gamma generated distributions such as gamma-Gumbel and gamma-normal distribution. Applications are stated as to why we need these distributions and some properties of these distributions have been derived. We have found out various properties of these distributions such as probability density function (pdf),Cumulative distribution function (cdf), survival function and hazard rate function. Expansions of pdf and cdf, asymptotes, quantile function, moment, extreme values, reliability, mean, median, mode, moment generating function, order statistics, Renyi and Shannon Entropy, bivariate generalizations and Maximum likilihood estimator (MLE). We also propose some theorems pertaining to moment of these distributions.