The Bias in Certain Estimates of the Parameters of the Extreme-Value Distribution

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.