Hypothesis Testing for the Scale-Exponential Family of Distributions
Parsa H. Rafsanjani, Adel Mohammadpour
We introduce a unified framework for hypothesis testing within the scale-exponential family of distributions, a continuous family that encompasses many well-known distributions as special cases. Uniformly most powerful tests are constructed for simple and one-sided hypotheses. For two-sided alternatives, where a UMP test does not typically exist, a uniformly most powerful unbiased test is derived. We also develop a test for the more complex task of testing against a composite interval hypothesis. The algorithms for these tests are implemented in the R programming language and are applied to a wide range of examples, demonstrating the framework's utility and comparing its performance across different distributions.
