[R] About Cumulant Generating Functions
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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