when i saw the expression below, i mistook it for kurtosis, partly because it came with two example graphs and their values for this metric.
$E[(X - E[X])^{3}]$
this supposedly measures skew, but i am having trouble understanding why. the value is 0 when perfectly symmetric, positive when right skewed and negative when left skewed. i have tried expanding the expression, but it didn't make anything clearer to me. i've searched high and low for reference materials, but i can't find any for this particular expression.
any advice? thanks in advance.