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.

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.

But kurtosis does not measure peakedness at all. Rather, it measures the outlier (rare, extreme value) characteristic of distribution. as compared to that of a normal distribution. Please see here https://en.wikipedia.org/wiki/Talk:Kurtosis#Why_kurtosis_should_not_be_interpreted_as_.22peakedness.22 for a complete explanation.

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