Hi!
I would to generate random number for truncated Laplace PDF. I saw from
a report that a truncated distribution function can be expressed as
F_truncated(x)=F(x)-F(low)/ (F(upper)-F(low)) ; low <=x
<=upper
For Laplace distribution function, F(x) can have
F(x) = 1/2 * exp(-(a-x)/b) for x<a
and F(x)=1-(1/2)*exp(-(x-a)/b) for x>=a
where a and 2b^2 are the mean and variance respectively.
So I generate random variates having distribution function F_truncated
is as follows,
(1) Generate U ~ U(0, 1).
(2) Set Y = F(low) + [F(upper) - F(lower)]U.
(3) Return x = inverse F(Y).
It turns out that I have the following x
x=a + b * ln ( 2*(U*(F(upper)-F(low)) + F(low))); for x <a
x=a - b * ln ( 2*(1-U*(F(upper)-F(low)) - F(low))); for x >= a
However, when generated the outputs do not seems correct at all. I don't
know where had gone wrong. Thanks in advance for any help.
Best Regards,
Su
.
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