Performs Frosini test for the composite hypothesis of normality,
see e.g. Frosini (1987).
Usage
frosini.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 Frosini statistic.
p.valuethe p-value for the test.
methodthe character string "Frosini test for normality".
data.namea character string giving the name(s) of the data.
Details
The Frosini test for normality is based on the following statistic:
$$B_n = \frac{1}{\sqrt{n}}\sum_{i=1}^n{\left|\Phi(Y_i) - \frac{i-0.5}{n} \right|},$$
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
Frosini, B.V. (1987): On the distribution and power of a goodness-of-fit statistic with parametric and nonparametric applications, "Goodness-of-fit". (Ed. by Revesz P., Sarkadi K., Sen P.K.) --- Amsterdam-Oxford-New York: North-Holland. --- Pp. 133--154.