A simulation-based testing of difference in the means of gamma-distributed positive quantities

Abstract

This paper presents a simulation-based testing procedure that can be easily applied by practitioners who try to determine whether two gamma-distributed variables have the same expected values. From both theoretical and practical points of view, the gamma distribution and the testing in question have been of interest for some time given the many applications they can be used for, which include problems in the fields of economics, industrial statistics, life sciences, and others. The efforts to achieve the stated statistical objective have been focused throughout the years either on performing nontrivial, approximating mathematical steps or on simulations based on resampling techniques of various kinds. This text works with simulations that try to get closer to the true distributions of the quantities of interest so that a test can be designed rather than using samples generated out of samples, as the resampling techniques perform this by taking the initial samples for an approximation of the populations. The results presented in this text were validated, and they were also compared to other methods where possible. The resulting technique was looked upon as a complement to all the techniques that have been presented on this subject. The major advantage of the proposed procedure is seen in its simplicity. Since simulations are the basis for the presented conclusions, the results are unsurprisingly not as general as what could be achieved by exact mathematical deduction, but they do cover a reasonable range of situations that can serve as a basis on which to analogously build further research if desired.