EmpiricalDistribution

The distribution of the values actually observed in data.

EmpiricalDistribution(data)an inert distribution object wrapping data (a list).

Typed signatures

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

Domain: Statistics

Details

• PDF/CDF at $x$ are the observed PROPORTIONS — the count of data equal to (resp. at most) $x$, divided by its length. Wolfram's own PDF is a continuous, kernel-smoothed density; this is a discrete empirical measure instead, a documented divergence.
• Mean delegates to Mean of data; Variance is the population variance (divisor $n$), as in Wolfram, so it is $(n-1)/n$ of Variance(data).
• RandomVariate resamples uniformly from data, with replacement.

Examples

Basic #

2 of the 4 elements are 2

live ↗

In$\operatorname{PDF}(\mathrm{EmpiricalDistribution}(\bigl\lbrack1, 2, 2, 3\bigr\rbrack), 2)$Out$\frac{1}{2}$

live ↗

In$\operatorname{CDF}(\mathrm{EmpiricalDistribution}(\bigl\lbrack1, 2, 2, 3\bigr\rbrack), 2)$Out$\frac{3}{4}$

live ↗

In$\mathrm{mean}(\mathrm{EmpiricalDistribution}(\bigl\lbrack1, 2, 2, 3\bigr\rbrack))$Out$2$

live ↗

In$\mathrm{Variance}(\mathrm{EmpiricalDistribution}(\bigl\lbrack1, 2, 2, 3\bigr\rbrack))$Out$\frac{1}{2}$

About

Examples	4

See also: Mean, Variance, RandomVariate