Compute the Skewness

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Description

Provides three methods for performing skewness test.

Usage

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Skewness(x, na.rm = TRUE, type = 3)

Arguments

x

a numeric vector containing the values whose skewness is to be computed.

na.rm

a logical value for na.rm, default is na.rm=TRUE.

type

an integer between 1 and 3 for selecting the algorithms for computing the skewness, see details below.

Details

Skewness is a measure of symmetry distribution. Negative skewness (g_1 < 0) indicates that the mean of the data distribution is less than the median, and the data distribution is left-skewed. Positive skewness (g_1 > 0) indicates that the mean of the data values is larger than the median, and the data distribution is right-skewed. Values of g_1 near zero indicate a symmetric distribution.

Value

An object of the same type as x

Note

There are several methods to compute skewness, Joanes and Gill (1998) discuss three of the most traditional methods. According to them, type 3 performs better in non-normal population distribution, whereas in normal-like population distribution type 2 fits better the data. Such difference between the two formulae tend to disappear in large samples. Type 1: g_1 = m_3/m_2^(3/2).

Type 2: G_1 = g_1*sqrt(n(n-1))/(n-2).

Type 3: b_1 = m_3/s^3 = g_1 ((n-1)/n)^(3/2).

Author(s)

Daniel Marcelino, dmarcelino@live.com

References

Joanes, D. N. and C. A. Gill. (1998) Comparing measures of sample skewness and kurtosis. The Statistician, 47, 183–189.

Examples

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w <-sample(4,10, TRUE)
x <- sample(10, 1000, replace=TRUE, prob=w)
Skewness(x, type = 1)
Skewness(x, type = 2)
Skewness(x)

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