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First the power cosine distribution as introduced in (2.6) is considered, where
with
. Thus the probability density function for the polar angle is given as
|
(5.36) |
Calculating the cumulative distribution function results in
|
(5.37) |
A variate obeying an arbitrary distribution can be obtained using the inversion method [25]. A uniformly distributed variate
on
mapped by the inverse cumulative distribution function leads to the desired distribution [115]
|
(5.38) |
Since
is uniformly distributed on
as well, the random polar angle can also be generated by [66]
|
(5.39) |
Algorithm 5.2 summarizes the generation of a random polar angle following the probability density function (5.36).
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Up: 5.3 Generation of Random
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Otmar Ertl: Numerical Methods for Topography Simulation