Estimation of Parameters of Finite Mixture of Rayleigh Distribution by the Expectation‐Maximization Algorithm

Abstract

In the lifetime process in some systems, most data cannot belong to one single population. In fact, it can represent several subpopulations. In such a case, the known distribution cannot be used to model data. Instead, a mixture of distribution is used to modulate the data and classify them into several subgroups. The mixture of Rayleigh distribution is best to be used with the lifetime process. This paper aims to infer model parameters by the expectation-maximization (EM) algorithm through the maximum likelihood function. The technique is applied to simulated data by following several scenarios. The accuracy of estimation has been examined by the average mean square error (AMSE) and the average classification success rate (ACSR). The results showed that the method performed well in all simulation scenarios with respect to different sample sizes.

Bayesian Methods for Estimation the Parameters of Finite Mixture of Inverse Rayleigh Distribution

“…. .., K. Afterward, we assessed the appropriate number of components by calculating the Bayesian information criteria [13] according to the formula…”

“…If u 1 < min (1, A j ), where u 1 is a random number from the uniform distribution U(0, 1), then accept λ (new) . Note that the quantity p(λ (new) j ; X, η, β) is the density value of the posterior distribution with the parameters shown in equation (13). (ii) Move the sampler to W (new) with probability min (1, V), where…”

“…Testing the number of components to determine the exact structure of the mixture model was a vital tool to deal with the above problem [10,11]. In much the same direction, the most used way of handling the above issues is adding a latent variable that results in a complete data log likelihood rather than using the incomplete one [12,13], and then estimating the model parameters by the expectation maximization(EM) algorithm [14][15][16].…”

Effective of Renyi Entropy in Markov Basis for Independent Model

“…Step (5). Add the elements of Markov basis to the original matrix to find the elements of the fiber which is all the alternative matrix of the original contingency table for example add + = [6 7 6 1 15 6 ] = , then stop after the cells become negative numbers as follows:…”

“…(Ali Talib Mohammed 2019) they discussed how to estimate appropriate functions from statistical data, especially non-parametric data, as well as how to ensure the data are independent. (Ali T. Mohammed et al 2022) they discussed how to deal with complex data and the information attached to it through statistical analysis.. This paper presents an analysis of two-way contingency table data of Rheumatoid arthritis using MBIM to find the alternatives to the real baseline arthritis data matrix and then test these alternatives to find the most independent alternative through the Renyi entropy information law.…”