| Value | Meaning |
|---|---|
| online | Similar to Welford's algorithm for updating variance, but adjusted for kurtosis. Can also put another KurtosisAccumulator of the same type, which uses the parallel algorithm from Terriberry that extends the work of Chan et al. |
| naive | Calculates kurtosis using (E(x^^4) - 4 * E(x) * E(x ^^ 3) + 6 * (E(x) ^^ 2) E(X ^^ 2) + 3 E(x) ^^ 4) / sigma ^ 2 (allowing for adjustments for population/sample kurtosis). This algorithm can be numerically unstable. |
| twoPass | Calculates kurtosis by first calculating the mean, then calculating E((x - E(x)) ^^ 4) / (E((x - E(x)) ^^ 2) ^^ 2) |
| threePass | Calculates kurtosis by first calculating the mean, then the standard deviation, then calculating E(((x - E(x)) / (E((x - E(x)) ^^ 2) ^^ 0.5)) ^^ 4) |
| assumeZeroMean | Calculates kurtosis assuming the mean of the input is zero. |
| hybrid | When slices, slice-like objects, or ranges are the inputs, uses the two-pass algorithm. When an individual data-point is added, uses the online algorithm. |
Kurtosis algorithms.