Adjusted Jarque-Bera Test of Univariate Normality by Urzua (1996)

Given an univariate sample \(x\), it tests $$H_0 : x\textrm{ is from normal distribution} \quad vs\quad H_1 : \textrm{ not } H_0$$ using a test procedure by Urzua (1996), which is a modification of Jarque-Bera test.

norm.1996AJB(x, method = c("asymptotic", "MC"), nreps = 2000)

Arguments

x

a length-\(n\) data vector.

method

method to compute \(p\)-value. Using initials is possible, "a" for asymptotic for example.

nreps

the number of Monte Carlo simulations to be run when method="MC".

Value

a (list) object of S3 class htest containing:

statistic

a test statistic.

p.value

\(p\)-value under \(H_0\).

alternative

alternative hypothesis.

method

name of the test.

data.name

name(s) of provided sample data.

References

Urzúa CM (1996). “On the correct use of omnibus tests for normality.” Economics Letters, 53(3), 247--251. ISSN 01651765.

Examples

## generate samples from uniform distribution
x = runif(28)

## test with both methods of attaining p-values
test1 = norm.1996AJB(x, method="a") # Asymptotics
test2 = norm.1996AJB(x, method="m") # Monte Carlo