statistics - calulating sample excess kurtosis using R package fBasics -

i used fbasics package calculate sample excess kurtosis of simple vector [1,2,3]:

> library(fbasics) > x=c(1,2,3) > kurtosis(x) [1] -2.333333 attr(,"method") [1] "excess"

what calculated based on wikipedia http://en.wikipedia.org/wiki/kurtosis#sample_kurtosis, -1.5. wonder why fbaswics package gives different result?

thanks!

use kurtosis moments package instead.

> library(moments) > kurtosis(x) [1] 1.5

kurtosis momments computes estimator of pearson's measure of kurtosis. function implemented (if x numeric vector) follows:

n <- length(x) n * sum((x - mean(x))^4)/(sum((x - mean(x))^2)^2)

for excess of kurtosis use:

> kurtosis(x)-3 [1] -1.5

now, understand what's different in kurtosis form fbasics, @ code, use:

library(fbasics) methods("kurtosis") getanywhere("kurtosis.default")

and if x numeric vector, excess of kurtosis defined in kurtosis fbasics (actually timedate, see comment) as:

sum((x - mean(x))^4/as.numeric(var(x))^2)/length(x) - 3

i think you. question in comment looking basic statistical answer, i've pointed out r programming hints answer homework.

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