TriangularDistribution

The triangular distribution on $[a,b]$ with mode $c$ (defaulting to the midpoint).

TriangularDistribution({a, b})mode defaults to the midpoint

(a+b)/2

TriangularDistribution({a, b}, c)mode given explicitly.

Typed signatures

Type	Package	Applies
`(list<real>, real?) -> distribution`	`statistics`	always

Domain: Statistics

Details

$PDF(x) = 2(x-a)/((b-a)(c-a))$ for $x < c$ , $2(b-x)/((b-a)(b-c))$ otherwise — no boundary clamp against $a$ or $b$ (a documented divergence).
$CDF$ is the corresponding piecewise quadratic.
$Mean = (a+b+c)/3$ , $Variance = (a^2+b^2+c^2-ab-ac-bc)/18$ , both exact.
RandomVariate samples via inverse transform.