Discriminating between log-normal and log-logistic distributions in the presence of type-II censoring

Bishal Diyali, Devendra Kumar and Sukhdev Singh ()
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Bishal Diyali: Central University of Haryana
Devendra Kumar: Central University of Haryana
Sukhdev Singh: Thapar Institute of Engineering and Technology

Computational Statistics, 2024, vol. 39, issue 3, No 16, 1459-1483

Abstract: Abstract The log-normal and the log-logistic distributions are two of the most commonly used distributions for studying positively skewed lifetime data. Both the distributions share number of interesting properties, and for a certain range of parameters their cumulative and hazard functions can also be similar in nature. However, selecting a more appropriate distribution and discriminating among them for a given data to best fit is an important issue. Further, when the data are observed in the presence of some censoring scheme the problem becomes more challenging. In this paper, we address the problem of selecting a more appropriate distribution by discriminating based on the random samples drawn in the presence of type-II censoring. We consider the difference of the maximized log-likelihood functions, and compute the asymptotic distribution of the discrimination statistic. We further propose a modified discriminating approach, and compute the probabilities of correct selection to check the performance of the discrimination procedure. Finally, simulation study is conducted, and two real data sets are analysed for the illustration purpose.

Keywords: Asymptotic distribution; Probability of correct selection; Likelihood ratio statistic; Model selection; Log-normal and log-logistic distributions (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00180-023-01351-7

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