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normtest (version 1.1)

hegazy1.norm.test: Hegazy--Green test for normality

Description

Performs Hegazy--Green test for the composite hypothesis of normality, see e.g. Hegazy and Green (1975).

Usage

hegazy1.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:
  • statisticthe value of the Hegazy--Green statistic.
  • p.valuethe p-value for the test.
  • methodthe character string "Hegazy-Green test for normality".
  • data.namea character string giving the name(s) of the data.

Details

The Hegazy--Green test for normality is based on the following statistic: $$T_1 = \frac{1}{n}\sum_{i=1}^n{\left|Y_{i}-\Phi^{-1}{\left(\frac{i}{n+1}\right)}\right|},$$ where $$Y_i=\frac{X_{(i)}-\overline{X}}{s}, \quad s^2=\frac{1}{n}\sum_{i=1}^n(X_i-\overline{X})^2.$$ The p-value is computed by Monte Carlo simulation.

References

Hegazy, Y. A. S. and Green, J. R. (1975): Some new goodness-of-fit tests using order statistics. --- Journal of the Royal Statistical Society. Series C (Applied Statistics), vol. 24, pp. 299--308.

Examples

Run this code
hegazy1.norm.test(rnorm(100))
hegazy1.norm.test(runif(100,-1,1))

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