kurtosis: Kurtosis Function

In modes: Find the Modes and Assess the Modality of Complex and Mixture Distributions, Especially with Big Datasets

Description

This function calculates the excess kurtosis of a data vector with optional bias correction. Kurtosis is a meaure of the peakedness or how heavy the tails of a distribution are–this dual interpretation is a result of the obvious inverse relationship between fat tails and high peaks. Excess kurtosis is simply "kurtosis-3." This is a correction that is often done to allow for comparision to the normal distribution–which has a kurtosis of 3 and excess kurtosis of 0. A kurtosis greater than 0 means that the distribution is leptokurtic and so has a high peak with skinny tails. Conversely, a kurtosis less than 0 means that the distribution is platykurtic and so has a low peak and heavy tails. This interpretation is slightly more complicated once the distribution is not unimodal and/or non-zero skewness. Comparing to Gaussian (normal) moments is more acceptable in these cases.

Usage

kurtosis(x, finite)

Arguments

x	Data vector.
finite	Should the finite sample correction (bias correction) be used? Defaults to TRUE.

Examples

data<-c(rnorm(15,0,1),rnorm(21,5,1))
hist(data)
kurtosis(data,TRUE)

Example output

[1] -2.103261

modes documentation built on May 2, 2019, 1:28 p.m.