Estimation of the Parameters of Power Function Distribution based on Progressively Type-II Right Censoring with Binomial Removal

• Published in: Statistica (Bologna) Vol. 82; no. 3; pp. 201 - 227
• Main Authors: E.I. Abdul Sathar, Sathyareji, G S
• Format: Journal Article
• Language: English
• Published: Bologna Università degli Studi di Bologna, Department of Statistical Sciences, Alma Mater Studiorum 01.09.2023; University of Bologna
• Subjects: Approximation; importance sampling procedure; lindley approximation; maximum likelihood distribution; Maximum likelihood method; Parameter estimation; power function distribution; prediction; Sampling techniques; Statistical prediction
• ISSN: 0390-590X; 1973-2201
• DOI: 10.6092/issn.1973-2201/12418

In this article, we proposed the estimates of unknown parameters of power function distribution in the context of progressive type-II censoring with binomial removals, where the number of units removed at each failure time follows a binomial distribution. The maximum-likelihood estimators (MLEs) for the power function parameters are derived using the expectation–maximization (EM) algorithm. EM-algorithm is also used to obtain the asymptotic variance-covariance matrix. By using the variance-covariance matrix of the MLEs, the asymptotic 950=0 confidence interval for the parameters are constructed. Bayes estimators under different loss functions are obtained using the Lindley approximation method and importance sampling procedure. We also introduced one and two sample prediction estimates and corresponding confidence intervals by using Bayesian techniques. To compare performance of the proposed estimators, we introduced simulation and real-life data studies.