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st: Creating a distribution from moments


From   Reza C Daniels <rdaniels@commerce.uct.ac.za>
To   statalist@hsphsun2.harvard.edu
Subject   st: Creating a distribution from moments
Date   Fri, 03 Nov 2006 12:08:23 +0200

Dear Statalisters,

I have summary statistics for four moments of the density of y: mean=877; std. deviation=611; skewness=0.658; kurtosis=2.278. Is it possible for me to use this information to generate a hypothetical density whose four moments approximate these values?

The analogy here would be creating, for example, a Gaussian distribution by:

set obs 1000
gen z1=invnorm(uniform())

My question relates to when one does not want a standard density but possibly some parameterization of a Beta or Gamma that fits the four moments.

I have searched through the probability distributions and density functions in Stata (I'm using version 8.2SE), but it is not immediately obvious to me that I can do this.

Any help would be appreciated.

Thanks,
Reza

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