Kurtosis

Kurtosis is the degree of peakedness of a distribution, defined as a normalized form of the fourth central moment of a distribution. There are several flavors of kurtosis commonly encountered, including the kurtosis proper, denoted or defined by

(1)

where denotes the th central moment (and in particular, is the variance). This form is implemented in Mathematica as Kurtosis[dist].

The kurtosis "excess" is denoted or , is defined by

(2)

and is implemented in Mathematica as KurtosisExcess[dist]. Kurtosis excess is commonly used because of a normal distribution is equal to 0, while the kurtosis proper is equal to 3.

Unfortunately, Abramowitz and Stegun (1972) confusingly refer to as the "excess or kurtosis."

Lepto-Kurtic: - If a curve is more peaked than normal curve then it is colled Lepto-Kurtic.

Platy-Kurtic: - If a curve is more flat-tapped than normal curve then it is called Platy-Kurtic.

Meso-Kurtic: -The curve representing a normal shape in a frequency distribution is called Meso-Kurtic.