spiegelhalter.norm.test: Spiegelhalter test for normality
Description
Performs Spiegelhalter test for the composite hypothesis of normality,
see Spiegelhalter (1977).
Usage
spiegelhalter.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 Geary statistic.
p.valuethe p-value for the test.
methodthe character string "Spiegelhalter test for normality".
data.namea character string giving the name(s) of the data.
Details
The Spiegelhalter test for normality is based on the following statistic:
$$T = \left( (c_nu)^{-(n-1)}+g^{-(n-1)} \right)^{1/(n-1)},$$
where
$$u=\frac{X_{(n)}-X_{(1)}}{s},
\quad
g=\frac{\sum_{i=1}^n|X_i-\overline{X}|}{s\sqrt{n(n-1)}},
\quad
c_n=\frac{(n!)^{1/(n-1)}}{2n},
\quad
s^2=\frac{1}{n-1}\sum_{i=1}^n(X_i-\overline{X})^2.$$
The p-value is computed by Monte Carlo simulation.
References
Spiegelhalter, D. J. (1977): A test for normality against symmetric alternatives. --- Biometrika, vol. 64, pp. 415--418.