Abstract
This paper attempts to estimate the parameters for the two-parameter Rayleigh distribution based on adaptive Type II progressive hybrid censored data with competing risks. Firstly, the maximum likelihood function and the maximum likelihood estimators are derived before the existence and uniqueness of the latter are proven. Further, Bayesian estimators are considered under symmetric and asymmetric loss functions, that is the squared error loss function, the LINEXloss function, and the general entropy loss function. As the Bayesian estimators cannot be obtained explicitly, the Lindley method is applied to compute the approximate Bayesian estimates. Finally, a simulation study is conducted, and a real dataset is analyzed for illustrative purposes.
Highlights
Reference [5] made the prediction from a two-parameter Rayleigh distribution based on doubly censored sample, derived the predictive distributions by adopting the Bayesian approach, and studied a numerical example to compare the effects of the hyperparameters
Interval estimation, and prediction for the two-parameter Rayleigh distribution have been well studied based on both complete data and censored data, scholars have not paid much attention to the estimation based on censored competing risks data, which is the theme of our paper
We focus on the point estimation of the parameters for the two-parameter Rayleigh distribution based on adaptive Type II progressive hybrid censored data with competing risks
Summary
The Rayleigh distribution, originally proposed by Lord Rayleigh in the field of acoustics, is one of the most important distributions when dealing with skewed data. When the location parameter μ is equal to zero, the two-parameter Rayleigh distribution degrades to the Rayleigh distribution This kind of flexibility is especially important when the lifetimes of the units do not begin from zero. Reference [4] studied confidence intervals for the parameters of the two-parameter Rayleigh distribution, solved the constrained optimization problems, and analyzed three numerical examples for illustrative purpose. Reference [5] made the prediction from a two-parameter Rayleigh distribution based on doubly censored sample, derived the predictive distributions by adopting the Bayesian approach, and studied a numerical example to compare the effects of the hyperparameters. Interval estimation, and prediction for the two-parameter Rayleigh distribution have been well studied based on both complete data and censored data, scholars have not paid much attention to the estimation based on censored competing risks data, which is the theme of our paper
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