Question

I have a probability density function, 2*x^2 * exp(-2/3*x^3) normalized from 0 to infinity. I want to generate a distribution according to this pdf over the range [a, b], how would I do this? I can create the distribution from 0 to infinity, I just can't map it into the interval [a, b], or just create it in that interval to begin with.

Answer 1

I really don't have a background in statistics, so I probably won't be much help. But I think that an important question to ask yourself is "just What properties of my original pdf do I want in my new pdf?". Obviously not everything can be the same, but maybe you can in some sense preserve the variance or skew of the distribution. Maybe you need to think of exactly what mapping of [0,∞) to [a,b] you need, and *then* make your transformation.