Theoretical Distributions: Binomial, Poisson and Normal Distributions

Abstract

Although observations of natural processes and phenomena in the earth sciences may combine many complex and poorly understood factors, it is remarkable that their frequency distribution may closely follow one of a few theoretical models. Generally, a theoretical distribution may be useful as an idealisation or approximation for interpolation and for comparisons. More specifically a theoretical model provides equations from which useful statistics such as mean, variance and confidence estimates can be calculated. The theoretical probability distribution also permits statistical hypotheses to be tested.