ProbabilityDistribution

A distribution given directly by its density $pdf$ , over $x \in [min,max]$ (continuous) or $x \in \{min,\ldots,max\}$ (discrete, step size 1).

ProbabilityDistribution(pdf, {x, min, max})continuous, density pdf(x) over [min, max].

ProbabilityDistribution(pdf, {x, min, max, 1})discrete, mass pdf(x) over {min, ..., max} — step size pinned to 1.

Typed signatures

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

Domain: Statistics

Details

$pdf$ is used AS WRITTEN, not renormalized — same as Wolfram's own ProbabilityDistribution, which does not renormalize its pdf argument either; it is the caller's responsibility that it already integrates/sums to 1.
$PDF(v) = pdf|_{x=v}$ (substitution) inside $[min,max]$ , $0$ outside.
$CDF$ / $Mean$ / $Variance$ go through compute-engine's own native Integrate (continuous) or Sum (discrete): exact whenever those resolve to a closed form, and left UNEVALUATED (not approximated) when they don't — numeric approximation still reaches them through N, same as everywhere else in this package.
An arbitrary discrete step size (other than 1) is out of scope for this head.