Estimating An Arbitrary Bivariate Distribution Directly

A distribution-free approach is developed for estimating a bivariate distribution function for an ore deposit in terms of the experimental grade correlogram and experimental "weight functions" of the deposit. These weight functions are calculated as part of the approximation used in the mononodal cutoff concept. Use of this method obviates the need to transform to an isofactorial bivariate model. The method is illustrated for two examples, where the bivariate distributions are supposedly known : (a) the bivariate normal distribution and (b) the bivariate lognormal distribution. It is shown that the estimate of the underlying bivariate distribution is optimal when working at the mononodal cutoff, as can be anticipated theoretically. The approximation decreases in quality on either side of the mononodal cutoff, but still remains acceptable as a first estimate of the actual bivariate distribution.