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.

中文翻译：

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瑞利分布的比例混合

本文介绍了瑞利（SMR）分布的比例混合。事实证明，这种新模型最初定义为两个独立随机变量的商，可以表示为瑞利和特定广义伽玛分布的比例混合。获得其pdf，cdf，弯矩，不对称性和峰度系数的闭合表达式。研究了其寿命分析，性质和Rényi熵。提出了基于矩和最大似然（ML）的推理方法。实现了期望最大化（EM）算法以通过ML估计参数。该算法还用于仿真研究中，这说明了我们建议的良好性能。考虑了两个真实的数据集，其中表明SMR模型提供了很好的拟合度，并且更灵活，尤其是对于峰度而言，