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March, 1958 Limiting Distributions of Homogeneous Functions of Sample Spacings
Lionel Weiss
Ann. Math. Statist. 29(1): 310-312 (March, 1958). DOI: 10.1214/aoms/1177706734


Suppose $T_1, T_2, \cdots, T_n$ are the lengths of $n$ subintervals into which the interval $\lbrack 0, 1\rbrack$ is broken by $(n - 1)$ independent chance variables, each with a uniform distribution on $\lbrack 0, 1\rbrack$. Moran [1], Kimball [2], and Darling [3] have shown that if $r$ is a positive number, then the asymptotic distribution of $T_1^r + T_2^r + \cdots + T_n^r$ is normal. It is the purpose of this note to extend this result in two directions: more general functions of $T_1, \cdots, T_n$ are handled, and the joint distribution of several such functions is discussed. The proof is short and very simple.


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Lionel Weiss. "Limiting Distributions of Homogeneous Functions of Sample Spacings." Ann. Math. Statist. 29 (1) 310 - 312, March, 1958.


Published: March, 1958
First available in Project Euclid: 27 April 2007

zbMATH: 0086.35201
MathSciNet: MR98441
Digital Object Identifier: 10.1214/aoms/1177706734

Rights: Copyright © 1958 Institute of Mathematical Statistics

Vol.29 • No. 1 • March, 1958
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