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Computational Order Statistics
Colin Rose
Murray D. Smith

Using mathStatica [1], Rose and Smith [2] illustrate the automated derivation of the exact density of order statistics obtained from a random sample of size n on a continuous random variable. This article illustrates the new functionality in mathStatica to allow for discrete random variables. Moreover, by building on the new Piecewise capability in Mathematica, we are able to further generalise to the case of non-identically distributed random variables, thereby providing a completely flexible solution.

*Notebook


*PDF


*HTML

*Introduction

*1. Continuous Parent Distribution

*2. Discrete Parent Distribution (Function Form)

*3. Discrete Parent Distribution (List Form)

*4. Extensions and Forthcoming Features

*References

About the Authors
Colin Rose is director of the Theoretical Research Institute, Sydney. In 1998, he was a visiting scholar at Wolfram Research. His recent research interests relate to exact computational methods in mathematical statistics, and in particular, with application to the mathStatica project.

Murray D. Smith is an associate professor in the Discipline of Econometrics and Business Statistics at the University of Sydney. His recent research includes applications of computational algebra in statistics and the uses of copulas in modelling dependence structures in econometrics.

Colin Rose
Theoretical Research Institute
Sydney NSW 2023
Australia
colin@tri.org.au

Murray D. Smith
Econometrics and Business Statistics
The University of Sydney
Sydney NSW 2006
Australia
Murray.Smith@econ.usyd.edu.au


     
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