Extended Topp–Leone family of distributions as an alternative to beta and Kumaraswamy type distributions: Application to glycosaminoglycans concentration level in urine

Abstract

In this paper, we introduce a modified family of distributions that unifies three different families with only one tuning parameter; the so-called exp-[Formula: see text], Topp–Leone-[Formula: see text] and exp-half-[Formula: see text] families of distributions. We study mathematical properties of the proposed family, including linear representations, quantile function, probability weighted moments, reliability parameter and stochastic ordering. One of the corresponding parametric statistical model is outlined, with estimation of the parameters by the method of maximum likelihood and investigation for possible applications to glycosaminoglycans concentration level in urine over the beta Weibull and Kumaraswamy Weibull distributions. The goodness-of-fit of five other members of the family is also assessed. Regression model is also discussed using the proposed distribution and applied to establish the relationship between the glycosaminoglycans concentration level and age of the children.