# Computes the Kurtosis

### Description

Returns the kurtosis test for object x. For vectors, kurtosis(x) is the kurtosis of the elements in the vector x. For matrices kurtosis(x) returns the sample kurtosis for each column of x. For N-dimensional arrays, kurtosis operates along the first nonsingleton dimension of x.Returns the kurtosis test for object x. For vectors, kurtosis(x) is the kurtosis of the elements in the vector x. For matrices kurtosis(x) returns the sample kurtosis for each column of x. For N-dimensional arrays, kurtosis operates along the first nonsingleton dimension of x.

### Usage

1 |

### Arguments

`x` |
A numeric vector containing the values whose kurtosis is to be computed. |

`na.rm` |
A logical value indicating whether NA values should be stripped before the computation proceeds, the default is FALSE. |

`type` |
An integer between 1 and 3 selecting one of the algorithms for computing kurtosis detailed below. |

### Details

In a similar way of skewness, kurtosis measures the peakedness
of a data distribution. A distribution with zero kurtosis has a shape
as the normal curve. Such type of kurtosis is called mesokurtic, or
mesokurtotic. A positive kurtosis has a curve more peaked about the
mean and the its shape is narrower than the normal curve. Such type is
called leptokurtic, or leptokurtotic. Finally, a distribution with
negative kurtosis has a curve less peaked about the mean and the its
shape is flatter than the normal curve. Such type is called
platykurtic, or platykurtotic. To be consistent with classical use of
kurtosis in political science analyses, the default **type** is the
same equation used in SPSS and SAS, which is the bias-corrected
formula: **Type 2:** G_2 = ((n + 1) g_2+6) * (n-1)/(n-2)(n-3). When you set type to 1, the following equation applies: **Type 1:** g_2 = m_4/m_2^2-3. When you set type to 3, the following equation applies: **Type 3:** b_2 = m_4/s^4-3 = (g_2+3)(1-1/n)^2-3. You must have at least 4 observations in your vector to apply this function.

### Value

An object of the same type as `x`

.

### Note

**Skewness** and **Kurtosis** are functions to measure the third and fourth **central moment** of a data distribution.

### Author(s)

Daniel Marcelino

### References

Balanda, K. P. and H. L. MacGillivray. (1988) Kurtosis: A Critical Review. *The American Statistician,* **42(2), pp. 111–119.**

### See Also

`detail`

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### Examples

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