A gallery of distributions with relevance to quantitative prospect appraisal.
The relevance of these distributions can be summarized roughly into the following categories:
(1) Basic for success ratios (binomial and beta)
(2) For distribution of prospect properties, such as porosity (normal)
(3) Used for fieldsize distribution, source rock thickness, permeability, etc. (lognormal, pareto)
(4) Important for Monte Carlo simulation (rectangular, triangular and double-triangular, but also all of the above)
Continuous probability distributions come in two forms: (1) the probability density distribution (pdf, or the "smooth" histogram) and (2) the integral of the pdf, the Cumulative Distribution Function (cdf). The latter may not always be available in analytical form. For instance the normal distribution cdf can be calculated numerically only. The cumulative distribution of a variable may be displayed conveniently on a probability graph that helps to identify the type of distribution.
Discrete probability distributions (e.g. binomial) have a function similar to the pdf, but instead called the "probability mass function (pmf)". A histogram of a discrete probability function is a set of spikes. The cdf is a step function.
A pdf, and a histogram have an important requirement: The area under the curve has to be equal to one.