Abstract
The hybrid censoring is a mixture of type-I and type-II censoring schemes. This paper presents the statistical inferences of the inverse Weibull distribution parameters when the data are type-I hybrid censored. First, we consider the maximum likelihood estimates of the unknown parameters. It is observed that the maximum likelihood estimates can not be obtained in closed form. We further obtain the Bayes estimates and the corresponding highest posterior density credible intervals of the unknown parameters under the assumption of independent gamma priors using the importance sampling procedure. We also compute the approximate Bayes estimates using Lindley's approximation technique. The performance of the Bayes estimates have been compared with maximum likelihood estimates through the Monte Carlo Markov chain techniques. Finally, a real data set have been analysed for illustration purpose.
Highlights
Type-I and type-II are the two most popular censoring schemes which are in use for any life testing experiment
We provide point and interval estimates for the unknown parameters of an inverse Weibull (IW) distribution based on type-I hybrid censored samples
Since the maximum likelihood estimators (MLEs) of the unknown parameters α, λ can not be obtained in closed forms, it is not easy to derive the exact distributions of the MLEs
Summary
Type-I and type-II are the two most popular censoring schemes which are in use for any life testing experiment. Singh and Tripathi (2015) studied a two-parameter lognormal distribution using hybrid censored samples and derived various point and interval estimates of unknown lognormal parameters from classical and Bayesian viewpoint. Tripathi and Rastogi (2016) considered point and interval estimation of the unknown parameters of a generalized inverted exponential distribution and obtained various classical and Bayes estimates based on hybrid censored samples. We provide point and interval estimates for the unknown parameters of an inverse Weibull (IW) distribution based on type-I hybrid censored samples. Ateya (2017) and Ateya (2020) considered estimation of the unknown parameters of the IW distribution based on Balakrishnan’s unified hybrid censoring and generalized type-II progressive hybrid censoring schemes, respectively.
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