Abstract
This work will address the problem of estimating the parameters for the Nadaraj ah–Haghighi (NH) distribution using progressive Type-1 censoring (PT1C) utilizing Bayesian and non-Bayesian approaches. To apply PT1C, censoring times for each stage of censoring needed to be known before the experiment started. To solve this issue of censoring time selection, qauntiles from the NH lifetime distribution will be used as PT1C censoring time points. Maximum likelihood (ML) estimators (MLEs) and asymptotic confidence intervals (ACoIs) are produced with a focus on the censoring technique. Bayes estimates (BEs) and accompanying maximum posterior density (PD) credible interval estimations are also created via the squared error (SEr) loss function. The BEs are evaluated using the Markov Chain Monte Carlo (MCMC) technique and the Metropolis–Hasting (MH) algorithm. An analysis of an actual data set demonstrates the theoretical implications of MLEs and BEs for defined schemes of PT1C samples. Finally, simulation results will be used to compare the performance of the various recommended estimators.
Highlights
Expanding continuous univariate distributions through adding a few more shape parameters is an important way of better exploring the skewness and tail weights, as well as other features of the produced distributions
We utilize computer simulations to test the efficiency of estimation methodologies, MLE and Bayesian estimation, for something like the Nadaraj ah–Haghighi (NH) distribution using the progressive Type-1 censoring (PT1C) scheme
Throughout this paper, we looked at the NH distribution estimate and prediction under PT1C from both a classical and a Bayesian approach
Summary
Expanding continuous univariate distributions through adding a few more shape parameters is an important way of better exploring the skewness and tail weights, as well as other features of the produced distributions. Due to the recent trend, applied statisticians may create more extended distributions that yield superior goodness-of-fit metrics whenever fitted to real data rather than just the classical distributions. The exponential (Ex) model is likely the most commonly used statistical distribution for analysis of survival and reliability concerns. The above model was the earliest in the lifetime literature about which statistical methods became substantially explored. [1] recently presented a generalization of the Ex distribution known as the Nadaraj ah–Haghighi (NH) distribution. Both distribution function (cdf) and probability density function (pdf) are computed on the basis of Ref. [1] recently presented a generalization of the Ex distribution known as the Nadaraj ah–Haghighi (NH) distribution.
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