kurtosis, positive skewed and negative skewed for probability distribution When discussing probability distribution, I always read something such as excess kurtosis, positive kurtosis, positive skewed and negative skewed. What exactly do these concepts indicate? In practical applications, such as market return or something else, what can these characteristics tell us?
 A: Excess kurtosis $=$ kurtosis $-$ 3, since the normal distribution has kurtosis $=$ 3 (that is what the "excess" refers to). Also, kurtosis is always positive, so any reference to signs suggests they are saying that a distribution has more kurtosis than the normal. Skew indicates how asymmetrical the distribution is, with more skew indicating that one of the tails "stretches" out from the mode farther than the other does.
Practically: High kurtosis indicates a high propensity of a distribution to give you "outliers", in the sense that you will tend to get a lot of rather closely spaced outcomes, followed by a few, rare, way-out-there values. In the markets, this type of distribution can lull you into a sense of complacency, with well localized values most of the time, only to ruin your day with a crazy loss. For skewed distributions, a right-skew to a financial product indicates that its positive returns tend to be higher than its losses, for a simple example, which all other things being equal, is good.
