I need to calculate the skewness, kurtosis and 5th moment of a data set. Here are the definitions of skew and kurtosis:
$f_{skew} = \frac{\frac{\sum(Y_i - \bar Y)^3}{N}}{s^3}$
$f_{kurtosis} = \frac{\frac{\sum(Y_i - \bar Y)^4}{N}}{s^4}$
with $s$ defined as
$s^2 = \frac{\sum (Y_i - \bar Y)^2}{N}$
A moment about the mean, $x_0$, is:
$<(Y-Y_0)^j> = \sum_{i=1}^N p_i (Y_i - Y_0)^j $
My question is: using the definition of the moment, how do I compute $f_{skew}$ and $f_{kurtosis}$ and the $5$th moment?