|„r„x„p„y„}„~„Ђ„Ђ„t„~„Ђ„x„~„p„‰„~„Ђ„u „Ђ„„„Ђ„q„‚„p„w„u„~„y„u |
The implication of example 3 is that, if X has uniform distribution on
(0,1), i.e. a U(0,1) distribution, then Y=F-1(X) has distribution function F.
If we therefore have n independent random values x1,...,xn from a U(0,1)
distribution, and if we calculate yj=F-1(xj) for j=1,...,n, then y1,...,yn are n independent random values from a distributiuon with distribution functiion F.
All programming languages and packages provide a random number
generator which gives a sequence of pseudorandom numbers. These have
the properties of a sequence of independent random values from a U(0,1) distribution.
We can use these pseudorandom numbers x1,...,xn, which may be
considered to be n independent random values from a U(0,1) distribution, to generate independent samples from any continuous distribution.
Using the formal definition, for a transformation T: X ЃЁ Y, onto means
For any y Ѓё Y, there is x Ѓё X, such that (x, y) Ѓё T,
and one-to-one means
(x, y) and (x', y) Ѓё T implies x = x'.
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