SciencesPo (version 0.11.21)

skewness: Test for Skewness

Description

The function provides three features to perform a skewness test, see details below.

Usage

skewness(x, na.rm = TRUE, type = 2)

Arguments

x

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

na.rm

A logical value indicating whether NA values should be stripped before the computation proceeds.

type

An integer between 1 and 3 selecting one of the algorithms for computing skewness detailed below.

Value

• An object of the same type as x.

Details

The skewness is a measure of symmetry distribution. Intuitively, 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. The skewness function will ignore missing values in x for its computation purpose. 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).

References

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

See Also

detail.

Examples

skewness(c(100,200,300), type = 2)

skewness(c(100,200,300), type = 1)

skewness(c(100,200,300), type = 3)

w<-sample(4,10, TRUE)

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

skewness(x, type=2)

skewness(x, type=3)

detail(x)