Estimation under a finite mixture of modified Weibull distributions based on censored data via EM algorithm with application

Abstract

In this paper, the maximum likelihood estimates (MLE's) of the parameters of a finite mixture of modified Weibull ( distributions are obtained based on type-I and type-II censored samples using the EM algorithm. A simulation study is carried out to study the behavior of the mean squared errors. A real data set is introduced and analyzed using a mixture of two distributions and also using a mixture of two distributions. A comparison is carried out between the mentioned mixtures based on the corresponding Kolmogorov-Smirnov (K-S) test statistic to emphasize that the mixture model fits the data better than the other mixture model.

Estimation Using Suggested EM Algorithm Based on Progressively Type-II Censored Samples from a Finite Mixture of Truncated Type-I Generalized Logistic Distributions with an Application

“…Ateya and Alharthi in [10] studied the estimation problem under a finite mixture of modified Weibull distributions under type-I, type-II, and type-II progressive censoring schemes using the ordinary likelihood method which depends on the differentiation of the LF with respect to the parameters and without studying the identifiability property. Also, Ateya and Alharthi in [11] studied the estimation problem under the same mixture model under type-I and type-II censoring schemes using the EM algorithm without studying the type-II progressive censoring case. Ateya in [12] studied the identifiability property and the estimation problem using EM algorithm under a finite mixture of generalized exponential distribution under type-I and type-II censoring schemes without studying type-II progressive censoring case.…”

Interval Estimation in a Two Parameter Weibull Distribution Based on Type-2 Censored Data

“…Equations (14), (15), and (16) will facilitate the computation of the observed Fisher information matrix denoted by…”

“…Some of the common statistical distributions used to fit censored life data include Rayleigh [4], Gamma [5], Gumbel [6], logistic [7], lognormal [8], log-logistic [9], exponential [10], normal [11], Weibull [12] and [13], and Mixed Weibull [14].…”

Reliability inference for VGA adapter from dual suppliers based on contaminated type‐I interval‐censored data

“…Elmahdy and Aboutahoun proposed a new approach for parameter estimation of finite Weibull mixture distributions, in which the expectation and maximization (EM) algorithm‐based maximum likelihood estimation method and Bayesian estimation method were investigated. Ateya and Alharthi proposed EM algorithmic method to estimate the parameters of a finite mixture of modified Weibull distributions based on type‐I and type‐II censored data. Daniyal and Aleem studied the properties of the mixture with Burr type XII and Weibull distributions.…”