Translator Disclaimer
July, 1974 Generalized $h$-Statistics and Other Symmetric Functions
D. S. Tracy, B. C. Gupta
Ann. Statist. 2(4): 837-844 (July, 1974). DOI: 10.1214/aos/1176342774

Abstract

Dwyer's (1937) $h$-statistic is extended to the generalized $h$-statistic $h_{p_1\cdots p_u}$ such that $E(h_{p_1\cdots p_u}) = \mu_{p_1} \cdots \mu_{p_u}$, similar to the extension of Fisher's $k$-statistic to the generalized $k$-statistic $k_{p_1\cdots p_u}$ requiring $E(k_{p_1\cdots p_u}) = \kappa_{p_1} \cdots \kappa_{p_u}$. The $h$-statistics follow simpler multiplication rules than for $k$-statistics and involve smaller coefficients. Generalized $h$-statistics are studied in terms of symmetric means, unrestricted sums, and ordered partitions, and their relationships with generalized $k$-statistics are established. The statistics are useful in obtaining approximate forms for sampling distributions when parent population is not completely known.

Citation

Download Citation

D. S. Tracy. B. C. Gupta. "Generalized $h$-Statistics and Other Symmetric Functions." Ann. Statist. 2 (4) 837 - 844, July, 1974. https://doi.org/10.1214/aos/1176342774

Information

Published: July, 1974
First available in Project Euclid: 12 April 2007

zbMATH: 0292.62016
MathSciNet: MR362631
Digital Object Identifier: 10.1214/aos/1176342774

Rights: Copyright © 1974 Institute of Mathematical Statistics

JOURNAL ARTICLE
8 PAGES


SHARE
Vol.2 • No. 4 • July, 1974
Back to Top