TruncatedDistribution

$dist$ restricted to $[a,b]$ (continuous) or $(a,b]$ (discrete), renormalized.

TruncatedDistribution({a, b}, dist)restricts dist to [a, b] (continuous) or (a, b] (discrete), renormalized.

Typed signatures

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

Domain: Statistics

Details

$Z = CDF(dist,b) - CDF(dist,a)$ ; $PDF(x) = PDF(dist,x)/Z$ inside the support, $0$ outside.
A continuous base's support is the CLOSED interval $[a,b]$ ; a DISCRETE base's support is the right-HALF-OPEN interval $(a,b]$ — Wolfram's own convention (e.g. TruncatedDistribution[{2,5}, PoissonDistribution[3]] has support $\{3,4,5\}$ , not $\{2,...,5\}$ ). Both share the same normalizer $Z$ , since $CDF(x) = P(X \le x)$ either way.
$CDF(x) = (CDF(dist,x) - CDF(dist,a))/Z$ for $x$ in range, clamped to $0$ below and $1$ above.
$Mean$ is exact only where the base has a closed-form partial expectation this package knows: UniformDistribution (trivially — the truncated uniform IS $Uniform(a,b)$ ), NormalDistribution (the standard truncated-normal-mean identity), ExponentialDistribution (compute-engine native, via the memoryless shift identity). Any other base's $Mean$ stays unevaluated.
Variance is not implemented for this head (out of scope for this batch) — stays unevaluated.