Optimal confidence regions for the parameters of a general exponential class under Type-II progressive censoring

¹ Department of Statistics and Operations Research, Kuwait University, Al-Shadadiyya, Kuwait
² Department of Mathematics, The University of Jordan, Amman 11942, Jordan

^* Corresponding author: reem.aljarallah@ku.edu.kw

Received: 2 September 2023
Accepted: 25 January 2024

Abstract

Under Type-II progressively censored data, joint confidence regions are proposed for the parameters of a general class of exponential distributions. The constrained optimization problem based on such censoring data can be adopted to obtain confidence regions for the unknown parameters of this general class with minimized size and a predetermined confidence level. The area of confidence sets are minimized by solving simultaneous non-linear equations. Two real data sets representing the duration of remission of leukemia patients and water level exceedances by River Nidd at Hunsingore located in New York, are analyzed by fitting appropriate well-known models. Further, numerical simulation study is performed to explain our procedures and findings here.