A new (T-X$$^\theta$$) family of distributions: properties, discretization and estimation with applications

Abstract

AbstractIn this paper, a new class of distributions called the T-X$$^\theta$$ θ family of distributions for bounded—(0,1)—and unbounded—$$(0,\infty )$$ ( 0 , ∞ ) —supported random variables is suggested. Some special sub-models of the proposed family are utilized. A new sub-model is selected to be studied in details. The statistical properties of the suggested family including quantile function, moments, moment generating function, order statistics and Rényi entropy are discussed. The maximum likelihood method is provided to estimate the parameters of the distribution and a Monte Carlo simulation study is used. The discretized T-X$$^\theta$$ θ family provided many sub-families and sub-models. In addition, eight real data sets are utilized to demonstrate the flexibility of the proposed continuous and discrete family’s multiple sub models.