A Local Limit Theorem for the Wilcoxon Rank Sum

The Local Limit Theorem: A Historical Perspective

The local limit theorem describes how the density of a sum of random variables follows the normal curve. However the local limit theorem is often seen as a curiosity of no particular importance when compared with the central limit theorem. Nevertheless the local limit theorem came first and is in fact associated with the foundation of probability theory by Blaise Pascal and Pierre de Fer...

A Generalization of Wilcoxon Rank Sum Test

In this paper, we consider applying the Wilcoxon’s idea for the construction of the one-sample problem to the two-sample case. For this, we show that the location translation parameter becomes a median of the distribution of the difference of two independent random variables under the location translation model. Based on this fact, we construct generalized signed-rank statistics for the two sam...

Reproducibility Probability Estimation for the Wilcoxon-Rank-Sum Test

Riassunto: La stima della probabilità di riproducibilità (RP) di una significatività statistica consiste nella stima a posteriori della potenza, ed è un indicatore dell’affidabilità dei risultati dei test statistici. Si analizzano qui alcuni metodi per la stima, puntuale e per intervalli, della RP per il test di Wilcoxon, e si comparano tramite uno studio di simulazione. Si evince che la soluzi...

Generalizing the Wilcoxon rank-sum test for interval data

Some Observations on the Wilcoxon Rank Sum Test

This manuscript presents some general comments about the Wilcoxon rank sum test. Even the most casual reader will gather that I am not too impressed with the scientific usefulness of the Wilcoxon test. However, the actual motivation is more to illustrate differences between parametric, semiparametric, and nonparametric (distribution-free) inference, and to use this example to illustrate how man...