Definition
Let (x1, …, xn) be iid real random variables with the common cdf F(t). Then the empirical distribution function is defined as
where 1{A} is the indicator of event A. For a fixed t, the indicator 1{xi ≤ t} is a Bernoulli random variable with parameter p = F(t), hence is a binomial random variable with mean nF(t) and variance nF(t)(1 − F(t)). This implies that is an unbiased estimator for F(t).
Read more about this topic: Empirical Distribution Function
Famous quotes containing the word definition:
“No man, not even a doctor, ever gives any other definition of what a nurse should be than this—”devoted and obedient.” This definition would do just as well for a porter. It might even do for a horse. It would not do for a policeman.”
—Florence Nightingale (1820–1910)
“... if, as women, we accept a philosophy of history that asserts that women are by definition assimilated into the male universal, that we can understand our past through a male lens—if we are unaware that women even have a history—we live our lives similarly unanchored, drifting in response to a veering wind of myth and bias.”
—Adrienne Rich (b. 1929)
“The very definition of the real becomes: that of which it is possible to give an equivalent reproduction.... The real is not only what can be reproduced, but that which is always already reproduced. The hyperreal.”
—Jean Baudrillard (b. 1929)