Interval Estimations of the Two-Parameter Exponential Distribution. (17th April 2012)

• Record Type: Journal Article
• Authors: Jiang, Lai; Wong, Augustine C. M.
• Other Names: Thavaneswaran A. Academic Editor.
• Is Part Of: Journal of probability and statistics. Volume 2012(2012)
• Publication Date: 2012-04-17
• Subjects: Probabilities -- Periodicals; Mathematical statistics -- Periodicals; Mathematical statistics; Probabilities; Periodicals; 519
• DOI: 10.1155/2012/734575
• Languages: English
• ISSNs: 1687-952X

Abstract

Abstract : In applied work, the two-parameter exponential distribution gives useful representations of many physical situations. Confidence interval for the scale parameter and predictive interval for a future independent observation have been studied by many, including Petropoulos (2011) and Lawless (1977), respectively. However, interval estimates for the threshold parameter have not been widely examined in statistical literature. The aim of this paper is to, first, obtain the exact significance function of the scale parameter by renormalizing the p ∗ -formula. Then the approximate Studentization method is applied to obtain the significance function of the threshold parameter. Finally, a predictive density function of the two-parameter exponential distribution is derived. A real-life data set is used to show the implementation of the method. Simulation studies are then carried out to illustrate the accuracy of the proposed methods.