Accession Number:

ADA158151

Title:

B-Splines and Linear Combinations of Uniform Order Statistics.

Descriptive Note:

Technical summary rept.,

Corporate Author:

WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s):

Report Date:

1985-05-01

Pagination or Media Count:

28.0

Abstract:

It is shown in this document that the density of the sum of n independent random variables uniformly distributed on unequal intervals is given by a linear combination of n B-splines with constant coefficients. Another useful representation of the same density is given using de Boors definition of the discrete B-spline. It is also shown that the B-spline is the density of a linear combination of order statistics from the uniform distribution on 0,1. This interpretation of the B-spline allows one to establish easily validity of recurrence relations for densities and moments of linear combinations of order statistics as well as to state limit theorems both for B-splines and linear combinations. Examples given illustrate how asymptotic results for B-splines may be applied to linear combinations of order statistics. Using limit theorems of probability theory two examples of Curry and Schoenberg 1966 for B-splines are derived even in somewhat greater generality.

Subject Categories:

  • Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE