Abstract
This paper is concerned with the estimation of the Weibull generalized exponential distribution (WGED) parameters based on the adaptive Type-II progressive (ATIIP) censored sample. Maximum likelihood estimation (MLE), maximum product spacing (MPS), and Bayesian estimation based on Markov chain Monte Carlo (MCMC) methods have been determined to find the best estimation method. The Monte Carlo simulation is used to compare the three methods of estimation based on the ATIIP-censored sample, and also, we made a bootstrap confidence interval estimation. We will analyze data related to the distribution about single carbon fiber and electrical data as real data cases to show how the schemes work in practice.
Highlights
Schemes by using the maximum likelihood and Bayesian estimation methods. e authors in [7] addressed the estimation of Weibull generalized exponential distribution (WGED) parameters based on generalized order statistics, and they derived the submodels of generalized order statistics such as order statistics and record values
We propose different bootstrap confidence intervals (CI) of population parameters under the Maximum likelihood estimation (MLE) method based on adaptive Type-II progressive censoring scheme (ATIIPCS) data with binomial removal for the WGED as a bootstrap percentile (BP) and bootstrap-t (BT)
We discussed MLE, maximum product spacing (MPS), and Bayesian estimation to estimate the parameter problem of the WGED based on ATIIPCS with random removal
Summary
Assume a random variable X > 0 has WGED with a vector of parameter Θ (α, c, θ), and say that its cumulative distribution function (CDF) is given by. En, the number of units removed at each failure time follows a binomial distribution which is, for i Rm. E number of units removed at each failure time assumed to follow a binomial distribution with the following probability mass function: Pr. ri where 0 ≤ ri ≤ n − m − ij− 11rj. Using equation (10), the likelihood function for WGED based on ATIIPCS can be written as. With the use of equation (11), the product spacing function for WGED based on ATIIPCS can be written as. Let s(Θ) ln S1(xi: m: n, Θ), the partial derivatives by the MPS method of equation (19) are given as follows:. We propose different bootstrap CIs of population parameters under the MLE method based on ATIIPCS data with binomial removal for the WGED as a bootstrap percentile (BP) and bootstrap-t (BT). For more information about this algorithm, see [31, 32] and [15]
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