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Abstract
In this study, the estimation of parameters of a three‐parameter flexible reduced logarithmic‐inverse Lomax (FRL‐IL) distribution based on progressive type‐II right censored sample is studied. These methods include maximum likelihood estimations (MLEs) and Bayesian estimators. Approximate confidence intervals (ACIs) for the reliability and hazard functions are estimated based on the asymptotic distribution of maximum likelihood estimates (MLEs). In addition, two bootstrap CIs are also proposed. Bayesian estimates are obtained for symmetric and asymmetric loss functions such as squared error loss (SEL) and linear‐exponential (LINEX) loss functions. The Gibbs within Metropolis‐Hasting sampler procedure is applied using the Markov Chain Monte Carlo (MCMC) technique to get the Bayes estimates of the unknown parameters and their credible intervals (CRIs). Finally, a real‐life dataset that represents a group of patients with bladder cancer is considered an application of the proposed methods.
Highlights
In life testing and reliability experiments, experiments must be often terminated before all units on the test have failed
It leads us to the area of censoring, namely, some surviving units are removed from the experiment following a specific censoring scheme, and the final sample obtained is the censored sample, see Klein and Moeschberger [1]
Since our study will be on patients with bladder cancer, which requires us to reduce the number of experimental patients and the time of the lifetime experiment of these patients, we will apply the progressive type-II censoring scheme, which satisfies the requirements of obtaining good estimation by reducing the experimental time of patients and keeping some experimental patients from failure
Summary
In life testing and reliability experiments, experiments must be often terminated before all units on the test have failed. The removal of units before failure is very often a procedure due to limitations of time and cost associated with the experiment In such cases, in a lifetime test, it is impossible for experimenters to obtain the complete sample information in a short period of time. Therapies, and health services for patients with bladder cancer will emerge as awareness and funding for the disease growth For this reason, since our study will be on patients with bladder cancer, which requires us to reduce the number of experimental patients and the time of the lifetime experiment of these patients, we will apply the progressive type-II censoring scheme, which satisfies the requirements of obtaining good estimation by reducing the experimental time of patients and keeping some experimental patients from failure.
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