Fast Computation by Block Permanents of Cumulative Distribution Functions of Order Statistics from Several Populations

D. H. Glueck Department of Preventive Medicine and Biometrics, University of Colorado Denver, Denver, Colorado, USACorrespondence[email protected]

A. Karimpour-Fard Department of Preventive Medicine and Biometrics, University of Colorado Denver, Denver, Colorado, USA

J. Mandel Department of Preventive Medicine and Biometrics, University of Colorado Denver, Denver, Colorado, USA

L. Hunter Department of Preventive Medicine and Biometrics, University of Colorado Denver, Denver, Colorado, USA

K. E. Muller Department of Epidemiology and Health Policy Research, University of Florida, Gainesville, Florida, USA

Abstract

The joint cumulative distribution function for order statistics arising from several different populations is given in terms of the distribution functions of the populations. The computational cost of our formula in the case of two populations is still exponential in the worst case, but it is a dramatic improvement compared to the general formula by Bapat and Beg. In the case when only the joint distribution function of a subset of the order statistics of fixed size is needed, the complexity is polynomial, for the case of two populations.

Keywords:

Mathematics Subject Classification:

Primary 62E15, 65C60

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Fast Computation by Block Permanents of Cumulative Distribution Functions of Order Statistics from Several Populations

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Fast Computation by Block Permanents of Cumulative Distribution Functions of Order Statistics from Several Populations

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