ABSTRACT
In reliability and time-to-failure studies, the instantaneous failure rate is often an item of concern to investigators. Introduction of the threshold parameter creates complications when we seek to estimate lognormal parameters from sample data. Stedinger and Hoshi et al. have been concerned with estimation for the three-parameter lognormal distribution in connection with fitting hydrologic data. In the absence of regularity restrictions, asymptotic variances and covariances of maximum likelihood estimators of distribution parameters can be obtained by inverting the Fisher information matrix, in which elements are negatives of expected values of second partial derivatives of the likelihood function with respect to the parameters. The principal objection to moment estimators centers about the large sampling errors due to use of the second and third moments, plus the fact that as shown by Heyde the lognormal distribution is not uniquely determined by its moments.
