Piotr Kulczycki A Test for Comparing Distribution Functions with Strongly Unbalanced Samples Statistica, vol. LXII, nr 1, ss. 39-49, 2002
Streszczenie:
In statistical practice the problem of testing a hypothesis which states that two independent random variables have the same probability distribution occurs rather often. In typical applications, especially in the fields of economics and the life sciences, the sizes of the random samples obtained from populations with comparable distributions are similar, and this fact was the fundamental premise used in constructing the classical nonparametric tests. Yet with the expansion of computer technology in modern engineering, e.g. during work in the online regime in automatic control systems, the need has appeared for statistical inference regarding the equality of two distributions on the sole basis of one current value of the selected vector quantities, and thus in a case when one of the random samples is one element. The present paper will be devoted to this issue. A new test is proposed based on the kernel estimators technique and the methodology of order statistics. Simulation investigations indicate that its properties are more advantageous than in the case of the classical tests familiar from the literature.