em algorithm

One of the generalizations of the normal distribution is the unlimited Skew normal distribution, which is more flexible than the classical normal distribution. In contrast to the normal distribution, the unlimited skewed normal distribution is an asymmetric distribution and includes various types of skewness. Therefore, it is used in fitting different types of real data. Therefore, we study the moving average autoregressive time series process based on the asymmetric normal coefficients of the unbounded Skew, or SUN-ARMA process for short. Providing a hierarchical representation of the unbounded Skew normal distribution facilitates the simulation of this distribution in practice. The parameters of the asymmetric SUN-ARMA process are estimated using the maximum likelihood method with the EM algorithm approach. The performance and accuracy of the maximum likelihood method in estimating the parameters of the SUN-ARMA process is investigated based on the simulated data under different sample sizes. Also, using two real data series, the efficiency of SUN-ARMA process is studied in comparison with the classical autoregressive process of moving average with normal coefficients, and the results confirm the superiority of SUN-ARMA process in fitting asymmetric real data.

The EM algorithm is a powerful tool and generic useful device in a variety of problems for maximum likelihood estimation with incomplete data which usually appears in practice. Here, the term ``incomplete" means a general state and in different situations it can mean different meanings, such as lost data, open source data, censored observations, etc. This paper introduces an application of the EM algorithm in which the meaning of ``incomplete" data is non-precise or fuzzy observations. The proposed approach in this paper for estimating an unknown parameter in the parametric statistical model by maximizing the likelihood function based on fuzzy observations. Meanwhile, this article presents a case study in the electronics industry, which is an extension of a well-known example used in introductions to the EM algorithm and focuses on the applicability of the algorithm in a fuzzy environment. This paper can be useful for graduate students to understand the subject in fuzzy environment and moreover to use the EM algorithm in more complex examples.

In this paper, the problem of estimating unknown parameters is investigated when lifetime data following Poisson-exponential distribution under classical and Bayesian frameworks based on progressively type-II hybrid censored data. We compute point and associated interval estimates under classical and Bayesian approaches. For point estimates in the problem of estimation, we compute maximum likelihood estimators of model using Expectation-Maximization (EM) and Stochastic Expectation-Maximization (SEM) algorithms under classical approach, these algorithms are easily implemented. We compute Bayes estimates with the help of Lindley and importance sampling technique under informative and non-informative priors using different loss functions namely squared error, LINEX as well as general entropy in Bayesian framework. The associated interval estimates are obtained using the Fisher information matrix and Chen and Shao method respectively under classical and Bayesian approaches. We analysis real data set, and conduct Monte Carlo simulation study for the comparison of various proposed methods. Finally, we present a conclusion.