A family of extended half-distributions: Theory and applications

Abstract

In this paper, we introduce a new family of distributions which extends several new families of half-
distributions. Also, the family can be viewed as a general weighted family of distributions. Some
general mathematical properties of the family are obtained, involving the quantile function, (condi-
tional) moments, moment generating function, entropies, order statistics, record values and a bivariate
extension of the family. Different estimation procedures for the family parameters are discussed. Some
sub-models of the family that can accommodate various shapes for the hazard rate and density func-
tions are given. Using two reliability data sets, the potentiality of proposed sub-models of the family
is shown under the estimation procedures.
Keywords: General family of distributions, Weighted distribution, Moments, Distribution on a unit-
interval, Estimation methods, Reliability data.