On the use of the beta distribution in probabilistic resource assessments

Natural Resources Research
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Abstract

The triangular distribution is a popular choice when it comes to modeling bounded continuous random variables. Its wide acceptance derives mostly from its simple analytic properties and the ease with which modelers can specify its three parameters through the extremes and the mode. On the negative side, hardly any real process follows a triangular distribution, which from the outset puts at a disadvantage any model employing triangular distributions. At a time when numerical techniques such as the Monte Carlo method are displacing analytic approaches in stochastic resource assessments, easy specification remains the most attractive characteristic of the triangular distribution. The beta distribution is another continuous distribution defined within a finite interval offering wider flexibility in style of variation, thus allowing consideration of models in which the random variables closely follow the observed or expected styles of variation. Despite its more complex definition, generation of values following a beta distribution is as straightforward as generating values following a triangular distribution, leaving the selection of parameters as the main impediment to practically considering beta distributions. This contribution intends to promote the acceptance of the beta distribution by explaining its properties and offering several suggestions to facilitate the specification of its two shape parameters. In general, given the same distributional parameters, use of the beta distributions in stochastic modeling may yield significantly different results, yet better estimates, than the triangular distribution.

Additional publication details

Publication type Article
Publication Subtype Journal Article
Title On the use of the beta distribution in probabilistic resource assessments
Series title Natural Resources Research
DOI 10.1007/s11053-011-9153-1
Volume 20
Issue 4
Year Published 2011
Language English
Publisher Springer
Contributing office(s) Eastern Energy Resources Science Center
Description 12 p.
First page 377
Last page 388