I have a function f[t] which is a density function. It has a [0,2] interval and integrates to unity. I convolve f[t] with itself to get g[t]. It has a [0,4] interval and integrates to unity. All is well with that and I understand.
BUT, the boundary of g[t] shouild be on the interval [0,4/Sqrt[3]]. This is based upon both simulation and other analyses.
At present, the area of the g[t] function on the [4/Sqrt[3], 4] interval accounts for 1.4087% of the area under the curve. Not a “trivial” or “throwaway” amount.
Does anyone know of a way to “re-scale” or modify my convolved result g[t] so that all of the resultant area under the curve is on the [0,4/Sqrt[3]] interval?
Thank you, David. I appreciate your response. I was unaware of the TruncatedDistribution function. Unfortunately, if I do that, I literally do “truncate” the right hand tail of the result.
I am hoping to find a smooth distribution curve that is positive on the (0, 4/Sqrt[3])) inteval. I am not sure if this is possible.
Maybe you are you looking to redefine g[t], and have it be the sum of two random variables divided by a constant such that its maximum possible value is 4/Sqrt[3]:
This modifies the original problem however, and I’m not sure if this is what you are looking for.
