I've added a trapezoidal distribution to numpy.random for consideration, pull request 3770: https://github.com/numpy/numpy/pull/3770 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/Metrika2003VanDor... 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 The docstring for the proposed numpy.random.trapezoidal() is as follows: """ trapezoidal(left, mode1, mode2, right, size=None, m=2, n=2, alpha=1) Draw samples from the generalized trapezoidal distribution. The trapezoidal distribution is defined by minimum (``left``), lower mode (``mode1``), upper mode (``mode1``), and maximum (``right``) parameters. The generalized trapezoidal distribution adds three more parameters: the growth rate (``m``), decay rate (``n``), and boundary ratio (``alpha``) parameters. The generalized trapezoidal distribution simplifies to the trapezoidal distribution when ``m = n = 2`` and ``alpha = 1``. It further simplifies to a triangular distribution when ``mode1 == mode2``. Parameters ---------- left : scalar Lower limit. mode1 : scalar The value where the first peak of the distribution occurs. The value should fulfill the condition ``left <= mode1 <= mode2``. mode2 : scalar The value where the first peak of the distribution occurs. The value should fulfill the condition ``mode1 <= mode2 <= right``. right : scalar Upper limit, should be larger than or equal to `mode2`. size : int or tuple of ints, optional Output shape. Default is None, in which case a single value is returned. m : scalar, optional Growth parameter. n : scalar, optional Decay parameter. alpha : scalar, optional Boundary ratio parameter. Returns ------- samples : ndarray or scalar The returned samples all lie in the interval [left, right]. Notes ----- With ``left``, ``mode1``, ``mode2``, ``right``, ``m``, ``n``, and ``alpha`` parametrized as :math:`a, b, c, d, m, n, \\text{ and } \\alpha`, respectively, the probability density function for the generalized trapezoidal distribution is .. math:: f{\\scriptscriptstyle X}(x\mid\theta) = \\mathcal{C}(\\Theta) \\times \\begin{cases} \\alpha \\left(\\frac{x - \\alpha}{b - \\alpha} \\right)^{m - 1}, & \\text{for } a \\leq x < b \\\\ (1 - \\alpha) \\left(\frac{x - b}{c - b} \\right) + \\alpha, & \\text{for } b \\leq x < c \\\\ \\left(\\frac{d - x}{d - c} \\right)^{n-1}, & \\text{for } c \\leq x \\leq d \\end{cases} with the normalizing constant :math:`\\mathcal{C}(\\Theta)` defined as ..math:: \\mathcal{C}(\\Theta) = \\frac{2mn} {2 \\alpha \\left(b - a\\right) n + \\left(\\alpha + 1 \\right) \\left(c - b \\right)mn + 2 \\left(d - c \\right)m} and where the parameter vector :math:`\\Theta = \\{a, b, c, d, m, n, \\alpha \\}, \\text{ } a \\leq b \\leq c \\leq d, \\text{ and } m, n, \\alpha >0`. 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 growth, decay, and boundary ratio parameters of the generalized trapezoidal distribution further allow for non-linear behavior to be specified. References ---------- .. [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/Metrika2003VanDor... .. [2] van Dorp, J. R., Rambaud, S.C., Perez, J. G., and Pleguezuelo, R. H. (2007) An elicitation proce-dure for the generalized trapezoidal distribution with a uniform central stage. Decision AnalysisJournal. 4:156–166. Preprint available: http://www.seas.gwu.edu/~dorpjr/Publications/JournalPapers/DA2007.pdf Examples -------- Draw values from the distribution and plot the histogram: >>> import matplotlib.pyplot as plt >>> h = plt.hist(np.random.triangular(0, 0.25, 0.75, 1, 100000), bins=200, ... normed=True) >>> plt.show() """ I am unsure if NumPy encourages incorporation of new distributions into numpy.random or instead into separate modules, but found the exercise to be helpful regardless. Thanks, Jeremy