A New Formula for $k$-Statistics

I. J. Good

doi:10.1214/aos/1176343757

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Home > Journals > Ann. Statist. > Volume 5 > Issue 1 > Article

January, 1977 A New Formula for $k$-Statistics

I. J. Good

Ann. Statist. 5(1): 224-228 (January, 1977). DOI: 10.1214/aos/1176343757

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Abstract

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.