A Class of Exponential Rayleigh Distribution and New Modified Weighted Exponential Rayleigh Distribution with Statistical Properties

This paper deals with the mathematical method for extracting the Exponential Rayleighh  distribution based on mixed between the cumulative distribution function of Exponential distribution and  the cumulative distribution function of Rayleigh distribution using an application (maximum), as well as derived different statistical properties for  distribution, and present a structure of a new distribution based on a modified weighted version of Azzalini’s (1985) named Modified Weighted Exponential Rayleigh  distribution such that this new distribution is generalization of the  distribution and provide some special models of the  distribution, as well as derived different statistical properties for  distributio

Efficient Computation of Multivariate Rayleigh and Exponential Distributions

We propose an efficient approach for the computation of cumulative distribution functions of N correlated Rayleigh or exponential random variables (RVs) for arbitrary covariance matrices, which arise in the design and analysis of many wireless systems. Compared to the approaches in the literature, it employs a fast and accurate randomized quasi-Monte Carlo method that markedly reduces the computational complexity by several orders of magnitude as N or the correlation among the RVs increases. Numerical results show that an order of magnitude larger values of N can now be computed for. Its application to the performance analysis of selection combining is also shown