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3.2.3 Generalized Transformation Method:
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3.2 Other Distributions
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3.2.1 Transformation of probability
3.2.2 Transformation Method
Given a probability density
:
Find a bijective mapping
such that the distribution of
is
:
It is easy to see that
fulfills this condition, with
.
E
XAMPLE:
Let
Then
, with the inverse
. Therefore:
Sample
equidistributed in
.
Compute
.
Geometrical interpretation:
is sampled from an equidistribution
and
.
The regions where
is steeper (i.e.
is large) are hit more frequently.
Franz J. Vesely Oct 2005
See also:
"Computational Physics - An Introduction," Kluwer-Plenum 2001