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Kurtosis is a summary of the fatness of a distribution's tails,
often (almost always) using the Normal distribution as a
comparison. In a Normal distribution, the kurtosis is 3. The term
"excess kurtosis" refers to the difference
kurtosis(x, na.rm = TRUE, excess = TRUE, unbiased = TRUE)A numeric variable (vector)
default TRUE. Should missing data be removed?
default TRUE. If true, function returns excess kurtosis (kurtosis -3). If false, the return is simply kurtosis as defined above.
default TRUE. Should the denominator of the variance estimate be divided by N-1, rather than N?
A scalar value or NA
If kurtosis is smaller than 3 (or excess kurtosis is negative), the tails are "fatter" than Normal, the distribution is "spread wider" than the Normal. If kurtosis is greater than 3 (excess kurtosis positive), then the observations are packed more closely around the mean than in the normal distribution and few observations are found in the tails.
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. According to the US NIST, http://www.itl.nist.gov/div898/handbook/eda/section3/eda35b.htm, kurtosis is defined as
where var(x) is calculated with the denominator N, rather than N-1.
A distribution is said to be leptokurtic if it is tightly bunched in the center (spiked) and there are long, narrow tails representing extreme values that might occur.