Cumulant-Generating Function
المؤلف:
Abramowitz, M. and Stegun, I. A.
المصدر:
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover
الجزء والصفحة:
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19-2-2021
1704
Cumulant-Generating Function
Let 
be the moment-generating function, then the cumulant generating function is given by
where 
, 
, ..., are the cumulants.
If
 |
(3)
|
is a function of 
independent variables, then the cumulant-generating function for 
is given by
 |
(4)
|
REFERENCES:
Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 928, 1972.
Kenney, J. F. and Keeping, E. S. "Cumulants and the Cumulant-Generating Function" and "Additive Property of Cumulants." §4.10-4.11 in Mathematics of Statistics, Pt. 2, 2nd ed. Princeton, NJ: Van Nostrand, pp. 77-80, 1951.
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