Journal of Probability and Statistics
Volume 2012 (2012), Article ID 734575, 8 pages
Research Article

Interval Estimations of the Two-Parameter Exponential Distribution

Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON, Canada M3J 1P3

Received 11 November 2011; Revised 24 January 2012; Accepted 31 January 2012

Academic Editor: A. Thavaneswaran

Copyright © 2012 Lai Jiang and Augustine C. M. Wong. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.