How to generate distributions given, mean, SD, skew and kurtosis in R?

Question

Is it possible to generate distributions in R for which the Mean, SD, skew and kurtosis are known? So far it appears the best route would be to create random numbers and tra

Answer 1

This is an interesting question, which doesn't really have a good solution. I presume that even though you don't know the other moments, you have an idea of what the distribution should look like. For example, it's unimodal.

There a few different ways of tackling this problem:

1. Assume an underlying distribution and match moments. There are many standard R packages for doing this. One downside is that the multivariate generalisation may be unclear.

2. Saddlepoint approximations. In this paper:

   Gillespie, C.S. and Renshaw, E. An improved saddlepoint approximation. Mathematical Biosciences, 2007.

   We look at recovering a pdf/pmf when given only the first few moments. We found that this approach works when the skewness isn't too large.

3. Laguerre expansions:

   Mustapha, H. and Dimitrakopoulosa, R. Generalized Laguerre expansions of multivariate probability densities with moments. Computers & Mathematics with Applications, 2010.

   The results in this paper seem more promising, but I haven't coded them up.