[R] About Cumulant Generating Functions

Ott Toomet otoomet at econ.dk
Wed Feb 5 17:46:06 CET 2003


 | From: "Feng Zhang" <f0z6305 at labs.tamu.edu>
 | Hey, all
 | Can anybody tell me the definition or form of 
 | cumulant generating function for a series
 | of random variables x1, x2, ....?
 | I know the moment generationg function
 | is E[exp(tx)], and want to know the relationships
 | bw cumulants and moments.

This is the log of moment-generating function:

K(s) = log M(s) = E[exp(sx)]

It is closely related with central moments:

K'(0) = E[x]
K''(0) = Var x
K'''(0) = E[(x - Ex)^3]

this was true for K''''(0) too AFAIR, but not for further
derivatives (but check rather yourself).



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