Optimal confidence regions for the two-parameter exponential distribution based on records

• Main Authors: Asgharzadeh, Akbar, Bagheri, S. F., Ibrahim, Noor Akma, Abu Bakar, Mohd Rizam
• Format: Article
• Language: English
• Published: Springer 2020
• Online Access: http://psasir.upm.edu.my/id/eprint/86992/1/Optimal%20confidence%20regions%20for%20the%20two.pdf; http://psasir.upm.edu.my/id/eprint/86992/; https://link.springer.com/article/10.1007/s00180-019-00914-x

In this article, we propose two families of optimal confidence regions for the location and scale parameters of the two-parameter exponential distribution based on upper records. Constrained optimization problems are used to find the smallest-area confidence regions for the exponential parameters with a specified confidence level. Optimal prediction interval for the future records is also proposed. Two numerical examples as well as a simulation study, are presented for illustrative purposes. It is shown that the reduction in area of the optimal joint confidence region with respect to the existing confidence regions is substantial.