McDonald Rayleigh distribution with application

Statistical modeling of many phenomena is very important topic, especially the phenomena of survival, reliability, economic and financial. Many standard probability distributions lack superiority in modeling data sets of complex phenomenal. In recent years, the design of different forms of probability distributions has received wide attention by using different techniques in statistical theory. In this paper, McDonald family used to extend Rayleigh (McR) distribution. Some theoretical statistical properties of McR distribution were discussed, shape and scale parameters of McR distribution were estimated by maximum likelihood (ML) and E-Bayesian (EB) methods under square error (SE) and linear exponential (Linex) loss functions with three different kinds of hyper priors of distributions. In this paper, we propose the use of alternating direction method for image reconstruction from highly incomplete convolution data, where an image is reconstructed as a minimizer of an energy function that sums a TV term for image regularity and a least squares term for data.