Inverse Weibull-Poisson Distribution and Estimation of its Parameters in Type-II Censored Data

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OBEIDI R.; NASIRI P.

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Journal Paper

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Journal: JOURNAL OF STATISTICAL SCIENCES Year:2022 | Volume:16 | Issue:1 Page(s): 165-188

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Information Journal Paper

Title

Inverse Weibull-Poisson Distribution and Estimation of its Parameters in Type-II Censored Data

Author(s)

OBEIDI R. | NASIRI P. | Issue Writer Certificate

Keywords

Compound Distribution

Inverse Weibull Distribution

Type-II Censoring

Abstract

Introduction In lifetime studies consider that different components cause the failure of the unit/item under study but of the same type that is not entirely observed. In this case, the failure time of the unit/item is recorded and evaluated based on the information obtained from the observation and as the minimum value among other components affecting failure. The experimenter cannot identify the component that led to the unit’, s failure. In the study of series systems, the minimum component lifetime among the effective components leads to failure and is observed. In recent literature, Adamidis and Loukas (1998) used the geometric distribution function as the number of failure components and introduced a two-parameter exponential-geometric distribution with a descending failure rate. In applying compounding distributions of lifetime study, the experimenter may face the phenomenon of censoring. Because there are cases in which the units/items, although alive, are lost or removed. In this study, type-II of censoring has been investigated. Recently, the Inverse Weibull Distribution in censored data has been studied by Ateya (2017), Singh and Tripathi (2018). This paper presents the inverse Weibull-Poisson distribution function in the series system of the type-II censored sample. Material and Methods This paper considers the classical and Bayesian estimation of parameters of inverse Weibull-Poisson distribution function under the Type-II Censoring. Since the normal equations are not solved analytically, the EM algorithm, as the numerical method, is used in estimating the maximum likelihood methods. Little and Rubin (1983) showed that the EM algorithm is more reliable than the Newton-Raphson method in the case of incomplete data. Then, the Fisher information matrix for censored data is obtained with the principle of Louis (1982), and the approximate confidence intervals can be calculated. Parameters are estimated under the square error and LINEX loss functions while Gamma distribution is prior distribution. In Bayesian estimation, since the posterior distribution is not obtained in closed form, parameters are estimated with Markov chain Monte Carlo techniques and samples are generated by Gibbs sampling via the Metropolis-Hastings algorithm. Finally, the Bayesian confidence intervals are obtained using Kundu (2008), and the HPD intervals are constructed with Chen and Shao (1999) methods. Results and Discussion To evaluate the performance of estimators in terms of MSE’, s and their corresponding confidence intervals, it is generated 10000 samples for different sample sizes and three censoring schemes. Conclusion The simulation results show that with decreasing number of censors for a fixed sample size, the estimation of the parameters is closer to the actual values, and the MSE are reduced. Moreover, with an increasing sample size, the MSE of parameters is reduced for a fixed censoring scheme. For the 30% censoring scheme, Bayesian estimators of the parameters under the square error loss function have small MSE. The maximum likelihood estimators of parameters for the 10% censoring scheme have small MSE. The simulation results using confidence intervals show that the length of confidence intervals is reduced for a fixed sample size with decreasing number of censored. Moreover, the classical confidence intervals have the shortest interval length for all censoring schemes. The length of the HPD confidence intervals is shorter than the Bayesian confidence intervals.

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APA: Copy

OBEIDI, R., & NASIRI, P.. (2022). Inverse Weibull-Poisson Distribution and Estimation of its Parameters in Type-II Censored Data. JOURNAL OF STATISTICAL SCIENCES, 16(1 ), 165-188. SID. https://sid.ir/paper/1021425/en

Vancouver: Copy

OBEIDI R., NASIRI P.. Inverse Weibull-Poisson Distribution and Estimation of its Parameters in Type-II Censored Data. JOURNAL OF STATISTICAL SCIENCES[Internet]. 2022;16(1 ):165-188. Available from: https://sid.ir/paper/1021425/en

IEEE: Copy

R. OBEIDI, and P. NASIRI, “Inverse Weibull-Poisson Distribution and Estimation of its Parameters in Type-II Censored Data,” JOURNAL OF STATISTICAL SCIENCES, vol. 16, no. 1 , pp. 165–188, 2022, [Online]. Available: https://sid.ir/paper/1021425/en

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