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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.

In this article, we introduce a new class of slash distribution, the slashed moment exponential distribution. The proposed distribution can be seen as an extension of the moment exponential distribution proposed in Dara and Ahmad (2012). This extension is more flexible than the moment exponential distribution in terms of kurtosis of distribution. It arises as the ratio of two independent random variables, a moment exponential distribution in the numerator and a power of uniform distribution in the denominator. We study some probability properties, discuss moment and maximum likelihood estimations and derive the reliability function and hazard function. Finally, we present two real data applications indicating that the new distribution can improve the moment exponential and exponentiated moment exponential distributions in fitting real data.