Estimating the shape parameter of Topp-Leone distribution based on progressive type II censored samples

• Published in: Revstat Vol. 14; no. 4; p. 415
• Main Author: Baygud, Husam Awni
• Format: Journal Article
• Language: English
• Published: Instituto Nacional de Estatistica 01.10.2016; Instituto Nacional de Estatística | Statistics Portugal
• Subjects: Bayes estimate; Bayesian analysis; credible interval; Frequency distributions (Statistics); Lindley’s approximation; Markov chain Monte Carlo; Mathematical research; maximum likelihood estimate; Monte Carlo methods
• ISSN: 1645-6726; 2183-0371
• DOI: 10.57805/revstat.v14i4.196

* In this paper, classical and Bayesian point estimations of the Topp-Leone distribution shape parameter are studied when the sample is progressive Type II censored. The maximum likelihood estimator (MLE) of the unknown parameter is proposed. Since the MLE does not have an explicit form, an approximate MLE has been derived. The Bayes estimate and the associated credible interval are also studied. Lindley's method is proposed to approximate the Bayes estimate. The importance sampling technique is also proposed to approximate the Bayes estimate and to construct the associated credible interval. Monte Carlo simulations are performed to compare the performances of the proposed methods, and two data sets have been analyzed for illustrative purposes. Key-Words: * Bayes estimate; credible interval; Lindley's approximation; maximum likelihood estimate; Markov chain Monte Carlo. AMS Subject Classification: * 62N02, 62F15.