Methods for obtaining distributions of uranium occurrence from estimates of geologic features

The problem addressed in this paper is the determination of a quantitative estimate of a resource from estimates of fundamental variables which describe the resource. Due to uncertainty about the estimates, these basic variables are stochastic. The evaluation of random equations involving these variables is the core of the analysis process. The basic variables are originally described in terms of a low and a high percentile (the 5th and 95th, for example) and a central value (the mode, mean or median). The variable thus described is then generally assumed to be represented by a three-parameter lognormal distribution. Expressions involving these variables are evaluated by computing the first four central moments of the random functions (which are usually products and sums of variables). Stochastic independence is discussed. From the final set of moments a Pearson distribution is obtained; the high values of skewness and kurtosis resulting from uranium data require obtaining Pearson curves beyond those described in published tables. A cubic spline solution to the Pearson differential equation accomplishes this task. A sample problem is used to illustrate the application of the process; sensitivity to the estimated values of the basic variables is discussed. Appendices contain details of the methods and descriptions of computer programs