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

Abstract

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.

An Extension of the Fréchet Distribution and Applications

“…In light of the groundbreaking studies by Rogers and Tukey [21], Andrews et al [22] on slash distribution; multivariate slash models proposed in Gómez et al [23] or Arslan and Genc [24], slash methodology has been proven to be useful to increase the weight of tails of a baseline distribution. See for instance Reyes et al [25], Del Castillo [26], Zörnig [27], Olmos et al [28] for the half-normal and generalized half-normal, Astorga et al [19] for the generalized exponential distribution, Barranco-Chamorro et al [29] for the Rayleigh distribution, Barrios et al [30] for the power half-normal, Gui [31] for the Lindley, and Castillo et al [32] for weighted Lindley, among others. However, in this paper, the slash methodology is applied in such a way, that we get a class of distributions more flexible than Fréchet baseline distribution as for skewness and kurtosis.…”

Slash-Weighted Lindley Distribution: Properties, Inference, and Applications

“…Since the pioneering works by Rogers and Tukey [5] and Mosteller and Tukey [6], it has been applied to a number of symmetrical and skewed distributions. We can cite Gómez et al [7] for distributions with elliptical contours, Olmos et al [8] for the generalized half-normal distribution, Del Castillo [9] for the sum of independent logistic distributions, Reyes et al for the Birnbaum-Saunders distribution in [10,11] and for the normal distribution in [12], Barranco-Chamorro et al [13] for the generalized Rayleigh distribution in Wang and Genton [14] and in Arslan and Genc [15], who proposed multivariate versions based on the normal multivariate distribution, to cite only a few.…”