I want to investigate how my function
P behaves with different probability functions
rho as input variables.
Output = P[rho]
I have to do this in a scientific and systematic way. One way could be:
Observing that each propability function can be described by central moments
Start with the inspection of how the the output changes with the first central moment (expected value) while keeping all other moments constant.
Study how the Output changes with the second central moment (=variance), letting all other moments constant.
I want to find out which moments are relevant and which are not.
Do you have alternative suggestions or experience with this approach?
How can I create a function which has given central moments (for example, mu = 1, sigma = 1, gamma = 0, kurtosity = 2)? Is there a way to do it with Mathematica?
I have not studied mathematics, but as far as I can understand, there should be a solution for every set of central moments as long the HankelMatrix is positive-semi-definit (Hausdorff's moment problem).
But how do I get this solution?