the H and P value of standard normal distribution

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?

Thanks in advance!

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

Answer 1

[Brendan Hamm]

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]

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