Maximum likelihood estimators based on discrete component lifetimes of a k-out-of-n system

Anna Dembińska () and Krzysztof Jasiński ()
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Anna Dembińska: Warsaw University of Technology
Krzysztof Jasiński: Nicolaus Copernicus University

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2021, vol. 30, issue 2, No 7, 407-428

Abstract: Abstract This paper deals with parametric inference about the independent and identically distributed discrete lifetimes of components of a k-out-of-n system. We consider the maximum likelihood estimation assuming that the available data consists of component failure times observed up to and including the moment of the breakdown of the system. First, we provide general conditions for the almost sure existence of a strongly consistent sequence of maximum likelihood estimators (MLE’s). Then, we focus on three typical discrete failure distributions—the Poisson, binomial and negative binomial distributions—and prove that in these cases the MLE’s are unique, provided they exist, and that they are strongly consistent. Finally, we complete our results by Monte Carlo simulation study. Interestingly, the inference considered in the paper can be viewed as equivalent to one based on Type-II right censored discrete data. Therefore, our results can as well be applied to the case when Type-II right censored sample from a discrete distribution is observed.

Keywords: MLE; Inference; k-Out-of-n system; Poisson distribution; Binomial distribution; Negative binomial distribution; 62F10; 62N02; 62N05 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s11749-020-00724-0

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