Discriminating Among the Log-Normal, Weibull, and Generalized Exponential Distributions

Abstract

In this paper we consider the model selection/ discrimination among the three important lifetime distributions. All these three distributions have been used quite effectively to analyze lifetime data in the reliability analysis. We study the probability of correct selection using the maximized likelihood method, as it has been used in the literature. We further compute the asymptotic probability of correct selection and compare the theoretical and simulation results for different sample sizes and for different model parameters. The results have been extended for Type-I censored data also. The theoretical and simulation results match quite well. Two real data sets have been analyzed for illustrative purposes. We also suggest a method to determine the minimum sample size required to discriminate among the three distributions for a given probability of correct selection and a user specified protection level.

Sampling Plans Based on Truncated Life Test for a Generalized Inverted Exponential Distribution

“…One may also refer to Abouammoh and Table 8. Goodness-of-fit tests for different distributions Vol 14, No 2, June 2015, pp.183-195, © 2015 Alshingiti (2009), Dey and Kundu (2009) and Dey and Pradhan (2013) for various other applications of this data set. Now suppose a producer proposes a lot of ball bearing and claims that the specified median life of the ball bearings is 70 million revolutions.…”

The odd generalized exponential family of distributions with applications

“…Since it is the most attractive generalization of the exponential distribution, the GE model has received increased attention and many authors have studied its various properties and also proposed comparisons with other distributions. Some significant references are: Gupta and Kundu (2001a;2001b;2003;2004;2007;2008;, Kundu et al (2005), Nadarajah and Kotz (2006), Dey and Kundu (2009), Pakyari (2010) and . In fact, the GE model has been proven to be a good alternative to the gamma, Weibull and log-normal distributions, all of them with two-parameters.…”

Model Selection Based on Tracking Interval under Unified Hybrid Censored Samples

“…Several articles have been published on model selection based on complete data, for example, Kundu et al (2005) compared the log-normal and generalized exponential distribution using maximized likelihood method, Dey and Kundu (2009) considered the problem of discriminating among the log-normal, Weibull and generalized exponential distributions, Cox (1961) improved the classical hypothesis testing to compare the nonnested hypothesis, Vuong (1989) tested the equivalence of the two models using the expectation of the log-likelihood ratio of the two candidate models. The results in Vuong have been extended and applied in a number of ways, including, Vuong and Wang (1993), Lien (1987), Commenges et al (2008), Sayyareh et al (2011), Commenges et al (2012) and Panahi (2016).…”