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September, 1956 The Bias in Certain Estimates of the Parameters of the Extreme-Value Distribution
Bradford F. Kimball
Ann. Math. Statist. 27(3): 758-767 (September, 1956). DOI: 10.1214/aoms/1177728182

Abstract

This paper is mostly concerned with a modification of the maximum-likelihood estimate of the scale parameter of the extreme-value distribution for which the bias can be explicitly obtained. A formula for computing this bias is derived, and bias factors are tabulated for sample sizes from $n = 2$ to $n = 112.$ A brief comparison is made between this estimator and the optimum linear estimator for a sample of size $n = 6.$ Attention is called to a bias which results from the maximum-likelihood estimate of the second parameter, and formulas for the bias and the variance of this estimate are obtained. In the concluding section, the significance of certain aspects of the maximum-likelihood estimate of the scale parameter in practical applications is briefly discussed.

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Bradford F. Kimball. "The Bias in Certain Estimates of the Parameters of the Extreme-Value Distribution." Ann. Math. Statist. 27 (3) 758 - 767, September, 1956. https://doi.org/10.1214/aoms/1177728182

Information

Published: September, 1956
First available in Project Euclid: 28 April 2007

zbMATH: 0073.15105
MathSciNet: MR79869
Digital Object Identifier: 10.1214/aoms/1177728182

Rights: Copyright © 1956 Institute of Mathematical Statistics

Vol.27 • No. 3 • September, 1956
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