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In statistics, the empirical distribution function is the distribution function associated with the empirical measure of the sample. This cumulative distribution function is a step function that jumps up by at each of the data points. The empirical distribution function estimates the cumulative distribution function underlying of the points in the sample and converges with probability 1 according to the Glivenko–Cantelli theorem. A number of results exist to quantify the rate of convergence of the empirical distribution function to the underlying cumulative distribution function. == Definition == Let be independent, identically distributed real random variables with the common cumulative distribution function . Then the empirical distribution function is defined as 〔(PlanetMath )〕 : where is the indicator of event . For a fixed , the indicator is a Bernoulli random variable with parameter , hence is a binomial random variable with mean and variance . This implies that is an unbiased estimator for . However, in some textbooks,〔Coles, S. (2001) ''An Introduction to Statistical Modeling of Extreme Values''. Springer, p. 36, Definition 2.4. ISBN 978-1-4471-3675-0.〕〔Madsen, H.O., Krenk, S., Lind, S.C. (2006) ''Methods of Structural Safety''. Dover Publications. p. 148-149. ISBN 0486445976〕 the definition is given as 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「empirical distribution function」の詳細全文を読む スポンサード リンク
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