A new method for generating distributions with an application to exponential distribution

• Published in: Communications in statistics. Theory and methods Vol. 46; no. 13; pp. 6543 - 6557
• Main Authors: Mahdavi, Abbas, Kundu, Debasis
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 03-07-2017; Taylor & Francis Ltd
• Subjects: Economic models; Entropy; Exponential distribution; Fisher information matrix; Flexibility; Formulas (mathematics); Hazard rate function; Mathematical models; Maximum likelihood estimation; Parameters; Primary: 62E15; Probability distribution functions; Quantiles; Secondary: 62H10; Statistics; Survival function
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1080/03610926.2015.1130839

A new method has been proposed to introduce an extra parameter to a family of distributions for more flexibility. A special case has been considered in detail, namely one-parameter exponential distribution. Various properties of the proposed distribution, including explicit expressions for the moments, quantiles, mode, moment-generating function, mean residual lifetime, stochastic orders, order statistics, and expression of the entropies, are derived. The maximum likelihood estimators of unknown parameters cannot be obtained in explicit forms, and they have to be obtained by solving non linear equations only. Further, we consider an extension of the two-parameter exponential distribution also, mainly for data analysis purposes. Two datasets have been analyzed to show how the proposed models work in practice.