This paper considers the statistical inferences of inverse Weibull distribution under progressive type-Ⅱ censored sample, which is a common distribution in reliability analysis. Two commonly used parameter estimation methods, maximum likelihood estimation and Bayesian estimation, are used in this paper, along with the inverse moment estimation. First, we derive the maximum likelihood estimators of parameters and propose Newtown-Raphson iteration method to solve these estimators. Assuming that shape and rate parameters are independent and follow gamma priors, we further obtain the Bayesian estimators by Lindley approximation. We also derive the inverse moment estimators and construct the generalized confidence intervals using the generalized pivotal quantity. To compare the estimation effects of these methods, we implement Monte Carlo simulation with the help of MATLAB. The simulation results show that the Bayesian estimation method outperforms the other two methods in terms of mean squared error. Finally, we verify the feasibility of these methods by analyzing a set of real data. The results indicate that the Bayesian estimation method provides more accurate estimates than the other two methods.
Citation: Haiping Ren, Xue Hu. Estimation for inverse Weibull distribution under progressive type-Ⅱ censoring scheme[J]. AIMS Mathematics, 2023, 8(10): 22808-22829. doi: 10.3934/math.20231162
This paper considers the statistical inferences of inverse Weibull distribution under progressive type-Ⅱ censored sample, which is a common distribution in reliability analysis. Two commonly used parameter estimation methods, maximum likelihood estimation and Bayesian estimation, are used in this paper, along with the inverse moment estimation. First, we derive the maximum likelihood estimators of parameters and propose Newtown-Raphson iteration method to solve these estimators. Assuming that shape and rate parameters are independent and follow gamma priors, we further obtain the Bayesian estimators by Lindley approximation. We also derive the inverse moment estimators and construct the generalized confidence intervals using the generalized pivotal quantity. To compare the estimation effects of these methods, we implement Monte Carlo simulation with the help of MATLAB. The simulation results show that the Bayesian estimation method outperforms the other two methods in terms of mean squared error. Finally, we verify the feasibility of these methods by analyzing a set of real data. The results indicate that the Bayesian estimation method provides more accurate estimates than the other two methods.
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Haiping Ren, Xue Hu. Estimation for inverse Weibull distribution under progressive type-Ⅱ censoring scheme[J]. AIMS Mathematics, 2023, 8(10): 22808-22829. doi: 10.3934/math.20231162
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