numpy/numpy — pull request #3770 by jthetzel (2013-09-21 17:50:33+00:00)
Title: random.trapezoidal

Added a trapezoidal distribution to numpy.random for consideration.

Similar to the triangular distribution, the trapezoidal distribution may be used where the underlying distribution is not known, but some knowledge of the limits and mode exists. The trapezoidal distribution generalizes the triangular distribution by allowing the modal values to be expressed as a range instead of a point estimate.

The trapezoidal distribution implemented, known as the "generalized trapezoidal distribution," has three additional parameters: growth, decay, and boundary ratio. Adjusting these from the default values create trapezoidal-like distributions with non-linear behavior. Examples can be seen in an R vignette ( http://cran.r-project.org/web/packages/trapezoid/vignettes/trapezoid.pdf ), as well as these papers by J.R. van Dorp and colleagues:

1) van Dorp, J. R. and Kotz, S. (2003) Generalized trapezoidal distributions. Metrika. 58(1):85–97. Preprint available: http://www.seas.gwu.edu/~dorpjr/Publications/JournalPapers/Metrika2003VanDorp.pdf

2) van Dorp, J. R., Rambaud, S.C., Perez, J. G., and Pleguezuelo, R. H. (2007) An elicitation procedure for the generalized trapezoidal distribution with a uniform central stage. Decision Analysis Journal. 4:156–166. Preprint available: http://www.seas.gwu.edu/~dorpjr/Publications/JournalPapers/DA2007.pdf