Frequency distributions of element concentrations—I. Theoretical aspects

Abstract Distributions other than the lognormal, particularly the gamma distribution, may be more satisfactory for representing the frequency distributions of trace-element concentrations in mineral samples. A semiquantitative test was therefore devised for determining whether the lognormal or the gamma type provides the better approximation to an observed distribution. Further quantitative tests, which must be applied before a decision is made, are outlined. It is shown that a lognormal distribution of concentrations can arise only by accident in a body of fresh igneous rock, but can be generated in weathered material such as soil. A gamma distribution of concentrations, or at least a close approximation, can be generated in any mineral body on the basis of three reasonable assumptions. Some beta distributions of the first kind show promise for the representation of concentrations of major components in mineral samples of any type. The hyperbolic subgroup of beta distributions of the second kind merits consideration for those trace elements whose concentrations have a very large coefficient of variation.