The two sample problem: Exact distributions, numerical solutions, simulations

TL;DR

This paper addresses the two sample problem by proposing exact distributions, numerical solutions, and simulations, focusing on statistical tests involving nuisance parameters and similarity measures.

Contribution

It introduces a comprehensive approach combining exact distributions, numerical methods, and simulations for the two sample problem, extending classical solutions like Welch-Aspin and Fisher-Behrens.

Findings

Derived exact distributions for two sample tests

Developed numerical solutions for complex cases

Validated methods through simulations

Abstract

The work presented in this article suggests a solution to the two sample problem. Keywords: Two sample problem, Welch-Aspin solution, Fisher-Behrens problem, nuisance parameter, similarity, the Linnik phenomenon.