rockchalk (version 1.8.98)

kurtosis: Calculate excess kurtosis

Description

Kurtosis is a summary of the peakedness of a distribution. In a Normal distribution, the kurtosis is 3. The term "excess kurtosis" refers to the difference

Usage

kurtosis(x, na.rm = TRUE, excess = TRUE, unbiased = TRUE)

Arguments

x

A numeric variable (vector)

na.rm

default TRUE. Should missing data be removed?

excess

default TRUE. If true, function returns excess kurtosis (kurtosis -3). If false, the return is simply kurtosis as defined above.

unbiased

default TRUE. Should the denominator of the variance estimate be divided by N-1, rather than N?

Value

• A scalar value or NA

Details

kurtosis - 3

Many researchers use the term kurtosis to refer to "excess kurtosis" and this function follows suit by returning excess kurtosis. The user may avoid this by setting excess = FALSE, in which case kurtosis is returned.

If na.rm = FALSE and there are missing values, the mean and variance are undefined and this function returns NA.

The kurtosis may be calculated with the small-sample bias-corrected estimate of the variance. Set unbiased = FALSE if this is not desired. It appears somewhat controversial whether this is necessary, hence the argument unbiased. According to the US NIST, http://www.itl.nist.gov/div898/handbook/eda/section3/eda35b.htm, kurtosis is defined as mean((x - mean(x))^4) kurtosis = ___________________ var(x)^2

where var(x) is calculated with the denominator N, rather than N-1.

A distribution is said to be leptokurtotic if it is tightly bunched in the center (spiked) and there are long, narrow tails representing extreme values that might occur.