A New Class of Distributions for Modelling Continuous Positively Skewed Data Sets

Abstract

In this paper, we proposed a new class of distributions by introducing a new constant in the existing model. We discuss general properties of the family such as density function, quantile function and hazard rate function. We then discuss a member of the family considering the exponential distribution as baseline distribution. Various properties of the model such as quantile function, moments, moment generating function, order statistics, stress-strength parameter, and mean residual life function are discussed. We also discussed the mean, variance, skewness and kurtosis of the proposed model numerically. The expression for Rényi and Shannon entropies are also derived. The different methods of estimation such as maximum likelihood estimation, maximum product spacing and least squares estimates are used for the estimation of the unknown parameters of the proposed distribution.. The simulation study is performed to study the behaviour of the estimates based on their mean squared errors. Lastly, we apply our proposed model to two real data sets. © 2025, Thai Statistical Association. All rights reserved.