st: ksmirnov on Johnson SB

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st: ksmirnov on Johnson SB

Demetris Christodoulou
Dear all,

This question should be very easy for the experienced.

For a standardized Johnson SB with parameters (xi,l,g,d) it holds that:
     Y = (X - xi) / l
So that a unit normal Z can be represented as:
     Z = g + d * logit Y
In Stata terms:
    Y = invlogit((Z - g)/d)
    X = xi + l * invlogit((Z - g)/d)

Hence, to generate the SB:
gen SB = xi + l  * invlogit((invnormal(uniform()) - g)/d)

Now, to run a ksmirnov test on the normal cumulative density:
sum X
ksmirnov X  = normal((X-r(mean))/r(sd))

My question is how do you run the equivalent ksmirnov on the cumulative
SB?
I thought that I got the cumulative right but now I am not sure.

many thanks, Demetris

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