[R] Jarque-Bera and rnorm()

[Murali Menon]

Folks,

I'm a bit puzzled by the fact that if I generate 100,000 standard normal 
variates using rnorm() and perform the Jarque-Bera on the resulting vector, 
I get p-values that vary drastically from run to run. Is this expected? 
Surely the p-val should be close to 1 for each test?

Are 100,000 variates sufficient for this test?

Or is it that rnorm() is not a robust random number generator? I looked at 
the skewness and excess kurtosis, and the former seems to be unstable, which 
leads me to think that is why JB is failing.

Here are my outputs from successive runs of rjb.test (the robust Jarque Bera 
from the lawstat package).


>set.seed(100)

>y <- rnorm(100000);rjb.test(y);skewness(y)[1];kurtosis(y)[1]

        Robust Jarque Bera Test

data:  y
X-squared = 1.753, df = 2, p-value = 0.4162

[1] -0.01025744
[1] 0.0008213325

>y <- rnorm(100000);rjb.test(y);skewness(y)[1];kurtosis(y)[1]

        Robust Jarque Bera Test

data:  y
X-squared = 0.1359, df = 2, p-value = 0.9343

[1] -0.001833042
[1] -0.002603599

>y <- rnorm(100000);rjb.test(y);skewness(y)[1];kurtosis(y)[1]

        Robust Jarque Bera Test

data:  y
X-squared = 4.6438, df = 2, p-value = 0.09809

[1] -0.01620776
[1] -0.005762349


Please advise. Thanks,

Murali

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