2. Empirical law
In the sample framework, where X = (X1,...,Xn) has as components independent variables of the same law μ, we define the empirical law by posing :
where the notation δ(a) denotes the "mass" (+ 1) at point a; μn is therefore constructed by assigning each observed variable Xi the "probability" 1/n. This is a random probability law that approximates the theoretical lawμ.
The empirical...
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Empirical law
Estimation of the distribution function
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