normtest (version 1.1)

wb.norm.test: Weisberg--Bingham test for normality

Description

Performs Weisberg--Bingham test for the composite hypothesis of normality, see Weisberg and Bingham (1975).

Usage

wb.norm.test(x, nrepl=2000)

Arguments

x

a numeric vector of data values.

nrepl

the number of replications in Monte Carlo simulation.

Value

• A list with class "htest" containing the following components:
• statistic
  the value of the Weisberg--Bingham statistic.
• p.value
  the p-value for the test.
• method
  the character string "Weisberg-Bingham test for normality".
• data.name
  a character string giving the name(s) of the data.

Details

The Weisberg--Bingham test for normality is based on the following statistic: $$WB = \frac{(\sum_{i=1}^nm_iX_{(i)})^2/\sum_{i=1}^nm_i^2}{\sum_{i=1}^n(X_i-\overline{X})^2},$$ where $$m_i=\Phi^{-1}\left(\frac{i-3/8}{n+1/4}\right).$$ The p-value is computed by Monte Carlo simulation.

References

Weisberg, S. and Bingham, C. (1975): An approximate analysis of variance test for non-normality suitable for machine calculation. --- Technometrics, vol. 17, pp. 133--134.

Examples

wb.norm.test(rnorm(100))
wb.norm.test(runif(100,-1,1))