A Generalized Rayleigh Family of Distributions Based on the Modified Slash Model

• Main Authors: Inmaculada Barranco-Chamorro, Yuri A. Iriarte, Yolanda M. Gómez, Juan M. Astorga, Héctor W. Gómez
• Format: Article
• Language: English
• Published: MDPI AG 2021-07-01
• Series: Symmetry
• Subjects: generalized Rayleigh distribution; EM algorithm; kurtosis; maximum likelihood estimation; slashed generalized Rayleigh distribution
• Online Access: https://www.mdpi.com/2073-8994/13/7/1226

Specifying a proper statistical model to represent asymmetric lifetime data with high kurtosis is an open problem. In this paper, the three-parameter, modified, slashed, generalized Rayleigh family of distributions is proposed. Its structural properties are studied: stochastic representation, probability density function, hazard rate function, moments and estimation of parameters via maximum likelihood methods. As merits of our proposal, we highlight as particular cases a plethora of lifetime models, such as Rayleigh, Maxwell, half-normal and chi-square, among others, which are able to accommodate heavy tails. A simulation study and applications to real data sets are included to illustrate the use of our results.