Empirical estimates

A simple empirical estimate of the probability distribution is obtained from a sample of data by calculating the relative frequency $f_i=n_i/n$ of occurrence of each event $\{X=x_i\}$. In the limit of large sample sizes, these empirical estimates $\hat{p}(x_i)=f_i$ of the distribution provide increasingly accurate unbiased estimates of the population probabilty distribution. The empirical distribution can be displayed graphically by plotting bars of height $f_i$ for the different values $x_i$.