University of Newcastle upon Tyne

School of Mathematics and Statistics

Statistics Seminars 2005-2006

21 October 2005, L401, 3:15pm

Jordan Stoyanov

Plackett’s extremal probabilistic/statistical problem

 Abstract

Suppose that X and Y are two independent observations (random points on the real line), each chosen according to a distribution  F.  In 1947, Robin Plackett treated the following problem (Biometrika 34, 120-122). Assume that X, and hence Y, has zero mean and variance 1: find  F such that the average distance E(|X-Y|) between X and Y is maximal.

This (it turns out not easy!) problem and its non-trivial solution found by Plackett has attracted the attention of other probabilists/statisticians. The name Plackett’s problem is commonly used for problems of this kind for more than 50 years. There are several further developments in this area, including two doctoral dissertations (one in Germany from 1993 and one in USA from 2002).  

I will present a part of the available material in an understandable way, also showing how these problems are related to random sample studies and Bayesian analysis.  If time permits, some open problems will be outlined.      

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