Performs Jarque--Bera test for the composite hypothesis of normality,
see Jarque and Bera (1987).
Usage
jb.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 Jarque--Bera statistic.
p.valuethe p-value for the test.
methodthe character string "Jarque-Bera test for normality".
data.namea character string giving the name(s) of the data.
Details
The Jarque--Bera test for normality is based on the following statistic:
$$JB = \frac{n}{6}\left((\sqrt{b_1})^2 + \frac{(b_2-3)^2}{4}\right),$$
where
$$b_1 = \frac{\frac{1}{n}\sum_{i=1}^n(X_i - \overline{X})^3}{\frac{1}{n}(\sum_{i=1}^n(X_i - \overline{X})^2)^{3/2}},$$
$$b_2 = \frac{\frac{1}{n}\sum_{i=1}^n(X_i - \overline{X})^4}{\frac{1}{n}(\sum_{i=1}^n(X_i - \overline{X})^2)^2}.$$
The p-value is computed by Monte Carlo simulation.
References
Jarque, C. M. and Bera, A. K. (1987): A test for normality of observations and regression residuals. --- International Statistical Review, vol. 55, pp. 163--172.