Abstract
In this paper, the scale mixture of Rayleigh (SMR) distribution is introduced. It is proven that this new model, initially defined as the quotient of two independent random variables, can be expressed as a scale mixture of a Rayleigh and a particular Generalized Gamma distribution. Closed expressions are obtained for its pdf, cdf, moments, asymmetry and kurtosis coefficients. Its lifetime analysis, properties and Rényi entropy are studied. Inference based on moments and maximum likelihood (ML) is proposed. An Expectation-Maximization (EM) algorithm is implemented to estimate the parameters via ML. This algorithm is also used in a simulation study, which illustrates the good performance of our proposal. Two real datasets are considered in which it is shown that the SMR model provides a good fit and it is more flexible, especially as for kurtosis, than other competitor models, such as the slashed Rayleigh distribution.
Highlights
Rayleigh distribution is a continuous and positive distribution named after Lord Rayleigh
An extension of the R distribution is introduced following the general method to obtain distributions with a higher kurtosis coefficient than the slash version of the Rayleigh model proposed by Iriarte et al [10], and applied successfully by other authors: Reyes et al [11] to obtain the Generalized Modified slash model, Reyes et al [12] to get a generalization of Birnbaum–Saunders, Iriarte et al [13] and Segovia [14] to extend the quasi-gamma and power Maxwell distributions, respectively
Closed expressions are given for its main characteristics: pdf, cdf, moments and related coefficients
Summary
Rayleigh distribution is a continuous and positive distribution named after Lord Rayleigh An extension of the R distribution is introduced following the general method to obtain distributions with a higher kurtosis coefficient than the slash version of the Rayleigh model proposed by Iriarte et al [10], and applied successfully by other authors: Reyes et al [11] to obtain the Generalized Modified slash model, Reyes et al [12] to get a generalization of Birnbaum–Saunders, Iriarte et al [13] and Segovia [14] to extend the quasi-gamma and power Maxwell distributions, respectively. Throughout the different sections in this paper, it will be shown that the SMR distribution can be used for modeling positive, right skew data with a heavy right tail.
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