On the Use of the Beta Distribution in Probabilistic Resource Assessments |
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Authors: | Ricardo A Olea |
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Institution: | (1) U.S. Geological Survey, 12201 Sunrise Valley Dr., MS 956, Reston, VA 20192, USA |
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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. |
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