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January, 1980 A Characterization of the Exponential and Related Distributions by Linear Regression
Y. H. Wang, R. C. Srivastava
Ann. Statist. 8(1): 217-220 (January, 1980). DOI: 10.1214/aos/1176344905

Abstract

Let $X_1, \cdots, X_n (n \geqslant 2)$ be a random sample on a rv $X$, and $Y_1 < \cdots < Y_n$ be the corresponding order statistics. Define $Z_k = \frac{1}{n-k}\Sigma^n_{i=k+1}(Y_i - Y_k), 1 \leqslant k \leqslant n - 1, W_k = \frac{1}{k-1}\Sigma^{k-1}_{i=1}(Y_k - Y_i),$ $2 \leqslant k \leqslant n$. Using the properties $E(Z_k\mid Y_k = y) = \alpha y + \beta$ and $E(W_k\mid Y_k = y) = \alpha y + \beta$, a.e. $(dF)$, where $\alpha$ and $\beta$ are constants, we obtain characterizations of several distributions which include the exponential, the Pearson (type I) and the Pareto (of the second kind) distributions.

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Y. H. Wang. R. C. Srivastava. "A Characterization of the Exponential and Related Distributions by Linear Regression." Ann. Statist. 8 (1) 217 - 220, January, 1980. https://doi.org/10.1214/aos/1176344905

Information

Published: January, 1980
First available in Project Euclid: 12 April 2007

zbMATH: 0422.62010
MathSciNet: MR557568
Digital Object Identifier: 10.1214/aos/1176344905

Subjects:
Primary: 62E10

Keywords: characterization , exponential distribution , Linear regression , order statistics , Pareto distribution of second kind , Pearson type I distribution

Rights: Copyright © 1980 Institute of Mathematical Statistics

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Vol.8 • No. 1 • January, 1980
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