Higher Moments of a Maximum‐Likelihood Estimate

SUMMARY For a distribution depending on a single parameter the first four sampling moments of the maximum-likelihood estimate to orders N-2, N-3, N-3 and N-4 respectively are given. Expressions for the measures of skewness Y1 and y2 are also given. Several illustrative examples are included as a check on the heavy algebra. The paper extends earlier work by Haldane and Smith.