hegazy2.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
hegazy2.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:
$$T_2 = \frac{1}{n}\sum_{i=1}^n{\left(Y_{i}-\Phi^{-1}{\left(\frac{i}{n+1}\right)}\right)^2}.$$
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.