# the H and P value of standard normal distribution

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yue li on 28 Aug 2018
Edited: yue li on 28 Aug 2018
Hello,
I computed the pdf of a standard normal distribution, with parameters µ equal to 0 and σ equal to 1.
I used lillietest to test whether the norm data is normal distribution or not. Since norm is standard normal distribution, it should has H value=0. Why the H value=1, and p value is 0.0012?
Yue
x = [-3:.1:3];
norm = normpdf(x,0,1);
>> [H,P,KSSTAT,CV]=lillietest(norm)
H =
1
P =
0.0012
KSSTAT =
0.1523
CV =
0.1131

Brendan Hamm on 28 Aug 2018
The lillietest tests the null hypothesis that the data comes from a normal distribution against the alternative that it does not. You are not passing in data from a normal distribution, but rather the density function values at specified value of the random variable.
data = randn(100,1)
[H,P,KSSTAT,CV] lillietest(data)
yue li on 28 Aug 2018
Edited: yue li on 28 Aug 2018
Hello, Brendan Hamm,
Thank you so much for your great help!
I am taking the mean and std of the values on the y axis of the pdf, not the x axis, which is a fairly meaningless statistic.
Thanks!
Yue