Generate random number between 0 and 1 with (negative)exponential distribution
maxammann
Heyho,
I'm trying to generate a random number between 0.0 and 1.0 with exponential/negative exponential distribution. There is an article, which tells that you have to get the "quantile function". But the results are still greater than 1.0. So I would need to scale my equation somehow.
My goal is to generate a random number in a range, where for example higher/lower values have a higher probability. (The distribution should be scalable)
Related questions(don't truncate the result to [0,1]):
pjs
The negative exponential distribution has support on the range [0, ∞), so I'm interpreting your question as a request for a truncated negative exponential. The Cumulative Distribution Function for such a beast with lower limit l >= 0, upper limit h > l, and rate λ is
F(x) = (exp(-λl) - exp(-λx)) / (exp(-λl) - exp(-λh))
We can find the inversion by setting this equal to U, a uniform(0,1) random number, and solving for x:
X = -ln(exp(-λl) - (exp(-λl) - exp(-λh)) * U) / λ
Since you specified lower and upper limits of 0 and 1, respectively, this reduces to
X = -ln(1 - (1 - exp(-λ)) * U) / λ
Replace U with a call to your favorite U(0,1) generator and that's your algorithm for generating X's with the desired distribution.
Here's a histogram of 10,000 values generated with λ = 5. Smaller values of λ give a flatter distribution, larger values show a more rapid exponential drop off.
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