Consider for example the Exponential distribution with c.d.f. $F(x) = 1-e^{-\lambda x}$.
$F^{-1}(x)$ would be inverse cdf (quantile function). If I generate y=Fâ1(x) with x uniformily distributed on [0,1], then y will follow..
If I generate $y = F^{-1}(x)$ with x uniformly distributed on $0 \lt x \lt 1$, then y will follow the specific distribution.
So I have an idea but i don't know if it is realizable:
For different values of x, where $0 \lt x \lt 1$, if we can get 1000 random numbers with the equation, $y= F^{-1}(x)$. (lets assume, we get 10,4,5,77,2,11,10,....). Can we generate this 1000 random values in interval (for example) 0-100? Hence, whether it is possible to generate random numbers "inside an interval" for exponential (and other distributions, in particular Zipf distribution).
UPDATE: If we consider the Zipf Distribution that has (from Wikipedia): $ pdf(x) = \frac{1}{x^s \times H_{N,s}} $ $ cdf(x) = \frac{H_{x,s}}{H_{N,s}} $
where $s \gt 0$ is the scale parameter, H is the Harmonic number $H_{N,s} = \sum_{i=1}^N \frac{1}{i^s}$
How can i generate a random generator "inside an interval" (for example from 1 to 100)? Thank you