The nth k-statistic k_n is the unique symmetric unbiased estimator of the cumulant κ_n of a given statistical distribution, i.e., k_n is defined so that 〈k_n 〉 = κ_n, where 〈x〉 denotes the expectation value of x. In addition, the variance var(k_r) = 〈(k_r - κ_r)^2 〉 is a minimum compared to all other unbiased estimators. Most authors (e.g., Kenney and Keeping 1951, 1962) use the notation k_n for k-statistics, while Rose and Smith prefer k_n.

cumulant | h-statistic | kurtosis | mean | moment | normal distribution | polykay | sample central moment | skewness | statistic | unbiased estimator | variance