Simulation of a continuous random variable with an arbitrary distribution

Simulation of a discrete random variable

Need to get the implementation of sample of η:

y ^( ^r ^)			…
			…

- distribution law.

Depict the probability of this law on the real axis.

Next comes the uniform "shooting" over the interval [0, 1]:

1) n = One;

2) is generated by x _n - Implements a tion

;

3) announced the implementation of the value η ;

Since ξ uniformly distributed on [0, 1], the values ​​I y ^(r) will appear with a probability equal to the length of the segment , _. , Vol. e. p _r

Suppose we have to get the implementation of sample of η: is a given with m cerned monotonically increasing function.

Theorem (The inverse function). Let inverse function. If ξ ~ U (0, 1), , Then the random variable η will have a (right) distribution .

Proof: =

=. The third equality holds, as the case of strictly monotonically increasing transformation sign of inequality persists. The last equality is obvious from the figure.

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