Bayesian and non‐Bayesian inference of Weibull lifetime model based on partially observed competing risks data under unified hybrid censoring scheme

Abstract

In this paper, a competing risk model is analyzed based on unified hybrid censoring scheme (UHCS). It is assumed that the latent failure times follow Weibull distributions with a common shape and different scale parameters. The maximum likelihood estimates (MLEs) and approximate confidence intervals (ACIs) of the distributional parameters are obtained. Sufficient conditions under which the MLEs exist (uniquely) have been studied. Further, the Bayes estimates are obtained with respect to symmetric and asymmetric loss functions. The noninformative and informative prior distributions are considered for computing the approximate Bayes estimates. Furthermore, the highest posterior density (HPD) credible intervals have been obtained by using Markov Chain Monte Carlo (MCMC) method with the Gibbs sampling technique. The coverage probabilities for each confidence interval are computed. Then, hypothesis testing has been implemented using likelihood ratio statistic. A Monte Carlo simulation study is carried out to compare the performance of the proposed estimates. Finally, two real data sets are provided to illustrate the estimates.

Statistical inference for Nadarajah-Haghighi distribution under unified hybrid censored competing risks data

“…Average lengths (AL) of confidence intervals and coverage probabilities (CP) are used to make a comparison between the interval estimators. Using the method described in [26] , competing risks samples based on UPHC have been constructed.…”

“…The second direction involves the use of competing risks data under UHCS to estimate the parameters , and θ . For more details on recent studies using partially observed competing risks data, see [21] , [22] , [23] , [24] , [25] , [26] , and [27] .…”

Bayesian inference for the inverse Weibull distribution based on symmetric and asymmetric balanced loss functions with application

“…Conversely, for 𝜈 = 0 , it transforms into the Bayesian estimate relative to the SE loss function. Similarly, the Bayesian estimator under the BLINEX loss function, as depicted in (19), reduces to the maximum likelihood estimate at 𝜈 = 1 and corresponds to the asymmetric LINEX loss function at 𝜈 = 0. Likewise, under the BGE loss function in (20), the Bayesian estimator reduces to the maximum likelihood estimate at 𝜈 = 1 and corresponds to the GE loss function at 𝜈 = 0.…”

Inference for a general family of inverted exponentiated distributions under unified hybrid censoring with partially observed competing risks data

“…In reliability analysis, to get around the issue of model identifiability, many researchers assume that the causes of failure are independent. See, for example Panwar et al (2015), Ashour and Nassar (2017), Koley and Kundu (2017), Wang (2018), Wang and Li (2019), Mahto et al (2021), Dutta and Kayal (2022b), Dutta and Kayal (2022a) and Dutta et al (2023). However, in general, it is not easy to verify the assumption that the causes of failure are independent to each other.…”