pymc.Triangular#

class pymc.Triangular(name, *args, rng=None, dims=None, initval=None, observed=None, total_size=None, transform=UNSET, **kwargs)[source]#

Continuous Triangular log-likelihood.

The pdf of this distribution is

\[\begin{split}\begin{cases} 0 & \text{for } x < a, \\ \frac{2(x-a)}{(b-a)(c-a)} & \text{for } a \le x < c, \\[4pt] \frac{2}{b-a} & \text{for } x = c, \\[4pt] \frac{2(b-x)}{(b-a)(b-c)} & \text{for } c < x \le b, \\[4pt] 0 & \text{for } b < x. \end{cases}\end{split}\]

(Source code, png, hires.png, pdf)

../../../_images/pymc-Triangular-1.png

Support

\(x \in [lower, upper]\)

Mean

\(\dfrac{lower + upper + c}{3}\)

Variance

\(\dfrac{upper^2 + lower^2 +c^2 - lower*upper - lower*c - upper*c}{18}\)

Parameters
lowertensor_like of float, default 0

Lower limit.

ctensor_like of float, default 0.5

Mode.

uppertensor_like of float, default 1

Upper limit.

Methods

Triangular.__init__(*args, **kwargs)

Triangular.dist([lower, upper, c])

Creates a tensor variable corresponding to the cls distribution.

Triangular.logcdf(lower, c, upper)

Compute the log of the cumulative distribution function for Triangular distribution at the specified value.

Triangular.moment(size, lower, c, upper)

Attributes

bound_args_indices

rv_class

rv_op