Empirical estimates

An empirical estimate of the population probability distribution can be obtained from a sample of data by calculating the cumulative frequencies of objects in the sample having values less than $x$. A cumulative frequency curve can be calculated either by accumulating up the frequencies in a histogram, or by sorting all the data into ascending order to get estimates of the empirical quantiles $x_q=\hat{F}^{-1}(q)$. In the limit of large sample sizes, these empirical estimates $\hat{F}(x)$ provide increasingly accurate unbiased estimates of the population probability distribution.