Custom Uniform Random Distribution
3 views (last 30 days)
Say I have a uniform random distribution in matlab using the rand() function.
How can I change the distribution for a given function such as 1/sqrt(x), so the distribution follows this curve?
I've tried to reject values but had no luck.
Roger Stafford on 24 Feb 2018
If you want to obtain a density distribution proportional to 1/sqrt(x) for x in some finite interval [a,b], you can proceed as follows. The cumulative probability function must be:
cdf(x) = (sqrt(x)-sqrt(a))/(sqrt(b)-sqrt(a))
which you get by integrating 1/sqrt(x) from a to x and adjusting the proportionality constant to get a cdf(b)=1 for the entire interval from a to b.
To generate this using rand, set the above cdf(x) to r = rand and solve for x:
r = rand;
%Solve for x in (sqrt(x)-sqrt(a))/(sqrt(b)-sqrt(a)) = r:
x = (sqrt(a)+(sqrt(b)-sqrt(a))*r).^2;
This illustrates how one would proceed to use rand for generating any given probability density function. It depends on being able to solve for x in an equation cdf(x) = r.