Definition
Distribution
In statistics, a distribution describes how probability or observed frequency is allocated across a space of possible values
. In machine learning, may be an instance space. Probability distribution
On a measurable space
, a probability distribution assigns each measurable set a probability . It describes a probabilistic model of values, whether specified in advance or fitted to data. Empirical distribution
Given observations
in , with , the empirical distribution assigns each measurable set its relative frequency in : The indicator
is when observation belongs to and otherwise. Each observation contributes mass ; repeated values contribute once per occurrence. Equivalently,
, where the point mass assigns to sets containing and to other sets. The empirical distribution is itself a probability measure, whereas is the data sequence used to construct it.