An Extension of J-Shaped Distribution with Application to Tissue Damage Proportions in Blood

Abstract

In this paper, we introduce a two parameter extension of J-shaped distribution investigated by Topp and Leone (J. Am. Stat. Assoc. 50, 209–219, 1995) which is defined on the unit interval. We explicitly derive the closed-form expressions of the moments, mode and quantiles of the proposed distribution. L-moments and coefficients of skewness and kurtosis are obtained using the quantile function. Other important properties including identifiability, entropy, stochastic orderings, stress-strength reliability and differential equations associated with the distribution are also discussed. We construct maximum likelihood estimators to estimate the distribution parameters that are unknown for a given set of practical data. An extensive simulation study is carried out to study the behaviors of mean squared error, bias and absolute bias of the maximum likelihood estimators. An application of modeling tissue damage proportions in blood at various concentration levels of a drug is presented to show the adequacy of the proposed distribution over the unit range distributions existing in the literature. A parametric regression model based on the proposed distribution is introduced and the goodness-of-fit results are compared with that of Beta regression model.