Change Points with Linear Trend in Exponential Family Distribution

Abstract

This paper considers the change point problem with linear trend in independent exponential family distributed random variables. It is interested to test if all random variables are identically distributed against there is a linear trend change at an unknown period of time among parameters of distribution of random variables. Testing procedures, which are considered, are two likelihood ratio-type approaches and the usual likelihood ratio approach. The test statistics are derived and their asymptotic behaviors are studied. Next, the power of three tests are compared and the conclusions are given . Testing procedures are studied in well-known distributions of exponential family. A real data example is also considered. This paper extends the Gupta and Ramanayake (2001) work in exponential distribution to the exponential family distribution.