# Definitions for **kurtosis**kɜrˈtoʊ sɪs

### This page provides all possible meanings and translations of the word **kurtosis**

### Random House Webster's College Dictionary

kur•to•siskɜrˈtoʊ sɪs(n.)

a measure of a curve describing the statistical frequency distribution in the region about its mode.

**Category:**Statistics

#### Origin of **kurtosis**:

1900–05; < Gk kýrtōsis convexity

### Wiktionary

kurtosis(Noun)

A measure of "peakedness" of a probability distribution, defined as the fourth cumulant divided by the square of the variance of the probability distribution.

**Origin:** From κύρτωσις, from κυρτός.

### Freebase

Kurtosis

In probability theory and statistics, kurtosis is any measure of the "peakedness" of the probability distribution of a real-valued random variable. In a similar way to the concept of skewness, kurtosis is a descriptor of the shape of a probability distribution and, just as for skewness, there are different ways of quantifying it for a theoretical distribution and corresponding ways of estimating it from a sample from a population. There are various interpretations of kurtosis, and of how particular measures should be interpreted; these are primarily peakedness, tail weight, and lack of shoulders. One common measure of kurtosis, originating with Karl Pearson, is based on a scaled version of the fourth moment of the data or population, but it has been argued that this measure really measures heavy tails, and not peakedness. For this measure, higher kurtosis means more of the variance is the result of infrequent extreme deviations, as opposed to frequent modestly sized deviations. It is common practice to use an adjusted version of Pearson's kurtosis, the excess kurtosis, to provide a comparison of the shape of a given distribution to that of the normal distribution. Distributions with negative or positive excess kurtosis are called platykurtic distributions or leptokurtic distributions respectively.

# Translation

#### Find a translation for the **kurtosis** definition in other languages:

Select another language:

#### Discuss these kurtosis definitions with the community:

# Citation

## Use the citation below to add this definition to your bibliography:

"kurtosis." *Definitions.net.* STANDS4 LLC, 2014. Web. 21 Dec. 2014. <http://www.definitions.net/definition/kurtosis>.