A new formula for cumulants was given by Good (1975). A short proof is now given and the result is used to obtain a new formula for $k$-statistics. This formula can be used both for deriving the expressions of $k$-statistics in terms of power sums of the observations, and for checking and locating errors in formulae that are already in the literature.
Publié le : 1977-01-14
Classification:
$k$-statistics,
cumulants,
permutations,
partitions,
permanents,
roots of unity,
62D05,
62H10
@article{1176343757,
author = {Good, I. J.},
title = {A New Formula for $k$-Statistics},
journal = {Ann. Statist.},
volume = {5},
number = {1},
year = {1977},
pages = { 224-228},
language = {en},
url = {http://dml.mathdoc.fr/item/1176343757}
}
Good, I. J. A New Formula for $k$-Statistics. Ann. Statist., Tome 5 (1977) no. 1, pp. 224-228. http://gdmltest.u-ga.fr/item/1176343757/