Testing for the Mixture Hypothesis of Conditional Geometric and Exponential Distributions

This study examines the mixture hypothesis of conditional geometric distributions using a likelihood ratio (LR) test statistic based on that used for unconditionalgeometricdistributions. Assuch,wederivethenulllimitdistribution of the LR test statistic and examine its power performance. In addition, we examine the interrelationship between the LR test statistics used to test the geometric and exponential mixture hypotheses. We also examine the performance of the LR test statistics under various conditions and confirm the main claims of the study using Monte Carlo simulations.