Empirical Distribution
Unlike probability distributions, which are theoretical, empirical distributions are based on observations.
Commonly, these observations are of repetitions of an experiment.
An empirical distribution describes:
- All observed values.
- The proportion of experiments in which each value occurred.
Unlike probability distributions, empirical distributions represent what actually happened in practice.
Empirical distribution of a die roll
As the number of die rolls increases, this distribution starts to look more like a uniform distribution due to the Law of Large Numbers.
Empirical distribution of a statistic
The empirical distribution of a Statistic is based on simulated values of the statistic. It describes:
- All observed values of the statistic.
- The proportion of samples in which each value occurred.
The empirical distribution of a statistic can be a good approximation to the Probability Distribution of the statistic, if the number of repetitions in the simulation is large.