A Numerical Maximum Likelihood Method for Estimating the Mean of a Compound Lognormal Distribution

Compound lognormal distributions serve as new generalized distribution laws for analyzing and estimating ore value distributions or related properties such as the average ore grade. These models are an alternative to the well known lognormal distribution. They are the translation of general geological constraints on the genesis of the deposit cumulated in suitable statistical properties. In this paper a maximum likelihood framework is established for estimating the parameters of such laws or parameter functions thereof. It is shown that under certain conditions maximum likelihood estimation is accurate and efficient in estimating the mean value even when relatively few samples are available. The method is based on a numerical maximization of the likelihood function of these models given the data. Confidence limits on these estimates are set up using resampling techniques such as the bootstrap. By this a complete methodology is presented for inference on ore grade distributions such as is shown in an example of gold data from the Merriespruit mine (South Africa) and the diamond size distribution of the Bougban deposit (Guinea).