Discriminating among inverse Weibull, lognormal, and inverse Gaussian distributions

• Published in: Quality and reliability engineering international Vol. 40; no. 4; pp. 1698 - 1718
• Main Authors: Diyali, Bishal, Kumar, Devendra, Singh, Sukhdev
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 01.06.2024
• Subjects: asymptotic distributions; Inverse Gaussian probability distribution; likelihood ratio test; Mathematical models; model selection; Parameters; probability of correct selection; SEM algorithm; Statistical analysis; Statistical distributions; Statistical tests
• ISSN: 0748-8017; 1099-1638
• DOI: 10.1002/qre.3484

Inverse Weibull, lognormal, and inverse Gaussian are some commonly used statistical distributions for modeling positively skewed failure lifetime data. These distributions share some interesting properties among themselves like they all have uni‐modal hazard rates. In this paper, we address the problem of discriminating among these statistical distributions to consider a more appropriate lifetime model. We first consider the complete samples and make use of the maximized log‐likelihood approach for choosing the correct model. We also obtain the expressions for logarithmic of defined test statistics, and associated asymptotic distributions. We then extend our discussion based on the observed sample in the presence of some censoring. We perform a simulation study in both cases to compare the probabilities of correct selection. Furthermore, for a given probability of correct selection and user‐specified protection level, we present a discussion to determine the minimum sample size required to discriminate among the three lifetime models. Finally, two real data sets are analyzed to illustrate the proposed methodology. In our findings, we observed that model parameters and methods of estimating unknown parameters play very important roles in the discrimination process, and sample size and the proportion of censoring become key factors to ensure a high probability of selecting a correct model.