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.
Highlights
In 1939 the Swedish engineer Walloddi Weibull published two papers on the strength of material in a series edited by the Royal Swedish Institute for Engineering Research
A certain generalization of the Weibull distribution is described in Mudholkar et al.[4] and applied to survival data
Exact coverage probabilities of approximate prediction intervals for the number of failures to be observed in a future inspection of a sample are evaluated in Nordman and Meeker [5]
Summary
Various distributional aspects of Weibull distribution is investigated in several recent papers. The modified Weibull distribution was proposed by Lai et al [17] as a new lifetime distribution. They have shown the capability of the model for modeling a bathtub shped hazard rate function. They characterized the model through the Weibull plot paper. They showed that the modified Weibull model compares well with other competing models to fit data that exhibit a bathtub shaped hazard rate function. A random variable T is said to have a finite mixture of MW distributions with parameters
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