Computes the Kurtosis

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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
kurtosis(x, na.rm = FALSE, type = 2)

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.

Examples

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kurtosis(c(100,200,300, 400), type = 2)

kurtosis(c(100,200,300, 400), type = 1)

kurtosis(c(100,200,300, 400), type = 3)

w<-sample(4,10, TRUE)

x <- sample(10, 1000, replace=TRUE, prob=w)

kurtosis(x, type=2)

kurtosis(x, type=3)

# see it in context.
detail(x)