Evidential Estimation of an Uncertain Mixed Exponential Distribution under Progressive Censoring

Abstract

In this paper, the evidential estimation method for the parameters of the mixed exponential distribution is considered when a sample is obtained from Type-II progressively censored data. Different from the traditional statistical inference methods for censored data from mixture models, here we consider a very general form where there is some uncertain information about the sub-class labels of units. The partially specified label information, as well as the censored data are represented in a united frame by mass functions within the theory of belief functions. Following that, the evidential likelihood function is derived based on the completely observed failures and the uncertain information included in the data. Then, the optimization method using the evidential expectation maximization algorithm (E2M) is introduced. A general form of the maximal likelihood estimates (MLEs) in the sense of the evidential likelihood, named maximal evidential likelihood estimates (MELEs), can be obtained. Finally, some Monte Carlo simulations are conducted. The results show that the proposed estimation method can incorporate more information than traditional EM algorithms, and this confirms the interest in using uncertain labels for the censored data from finite mixture models.

Parameter estimation of lifetime distribution for the meta-action unit with uncertainty failure modes under type-I censored data

“…The theory of belief function is a generalization of the theory of probability, 23 which can be used to express the support degrees assigned to some subsets (failure modes) in the domain O through the mass function h : 2 O ! ½0, 1.…”

“…The theory of belief function is a generalization of the theory of probability, 23 which can be used to express the support degrees assigned to some subsets (failure modes) in the domain Ω through the mass function h : 2 Ω → [ 0 , 1 ] . Compared to the probability models that are given to the atomic element of Ω , the mass function can be given to any subset of Ω .…”

“…19 In recent years, it has been applied to the classification, 20 decision making, 21 failure mode and effects analysis, 22 etc. Zhou and Shi 23 introduced the E2M algorithm to optimize the parameters estimation when the sample is obtained from Type-II progressively censored data. Different from the commonly adopted methods such as Bayes method or EM for the parameters estimation of mixed distributions, the estimation method based on the evidential likelihood function cooperates the uncertain information of the failure modes which can be used to express the possible degrees of the probability that each sample belongs to a sub-distribution.…”