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Empirical cumulative distribution function: a step function increasing by $1/n$ at each unique $X$-value that occurred in the sample.

10 votes
4 answers
13k views

What is the proper way to estimate the CDF for a distribution from samples taken from that d...

Given $n$ samples from a (continuous) distribution X, the obvious thing to do is sort them, and distribute them equally across $[0,1]$ by taking $(x_{(k)}, (k-1/2)/n)$ as estimates of particular poin …
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