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Inferences Based on Correlated Randomly Censored Gumbel’s Type-I Bivariate Exponential Distribution

Inferences Based on Correlated Randomly Censored Gumbel’s Type-I Bivariate Exponential Distribution The formal random censoring plan has been extensively studied earlier in statistical literature by numerous researchers to deal with dropouts or unintentional random removals in life-testing experiments. All of them considered failure time and censoring time to be independent. But there are several situations in which one observes that as the failure time of an item increases, the censoring time decreases. In medical studies or especially in clinical trials, the occurrence of dropouts or unintentional removals is frequently observed in such a way that as the treatment (failure) time increases, the dropout (censoring) time decreases. No work has yet been found that deals with such correlated failure and censoring times. Therefore, in this article, we assume that the failure time is negatively correlated with censoring time, and they follow Gumbel’s type-I bivariate exponential distribution. We compute the maximum likelihood estimates of the model parameters. Using the Monte Carlo Markov chain methods, the Bayesian estimators of the parameters are calculated. The expected experimental time is also evaluated. Finally, for illustrative purposes, a numerical study and a real data set analysis are given. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Data Science Springer Journals

Inferences Based on Correlated Randomly Censored Gumbel’s Type-I Bivariate Exponential Distribution

Krishna, Hare; Goel, Rajni
Annals of Data Science , Volume OnlineFirst – Jan 31, 2023
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Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
ISSN
2198-5804
eISSN
2198-5812
DOI
10.1007/s40745-023-00463-7
Publisher site
See Article on Publisher Site

Abstract

The formal random censoring plan has been extensively studied earlier in statistical literature by numerous researchers to deal with dropouts or unintentional random removals in life-testing experiments. All of them considered failure time and censoring time to be independent. But there are several situations in which one observes that as the failure time of an item increases, the censoring time decreases. In medical studies or especially in clinical trials, the occurrence of dropouts or unintentional removals is frequently observed in such a way that as the treatment (failure) time increases, the dropout (censoring) time decreases. No work has yet been found that deals with such correlated failure and censoring times. Therefore, in this article, we assume that the failure time is negatively correlated with censoring time, and they follow Gumbel’s type-I bivariate exponential distribution. We compute the maximum likelihood estimates of the model parameters. Using the Monte Carlo Markov chain methods, the Bayesian estimators of the parameters are calculated. The expected experimental time is also evaluated. Finally, for illustrative purposes, a numerical study and a real data set analysis are given.

Journal

Annals of Data Science – Springer Journals

Published: Jan 31, 2023

Keywords: Correlated random censoring; Gumbel’s type-I bivariate exponential distribution; Bayesian estimation; MCMC methods; Expected experimental time; 62N01; 62N02; 62F10; 62F15

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