Arrgh, Is it valid to generate ?m$p where p>q, and keep only the numbers which are less than q? (Not less than p.)
On Thu, Jul 16, 2020 at 11:27 AM Roger Hui <[email protected]> wrote: > A question for the statisticians and mathematicians among us. > > Suppose I want to generate uniform random numbers ?n$q. Is it valid to > generate ?m$p where p>q, and keep only the numbers which are less than p? > Assume that m can be as large as we like. > > An example where p is 30 and q is 10. > > x=: ?1e6$30 > y=: (x<10)#x > n=: #y > n > 332824 > c=: <: #/.~(i.10),y > +/c > 332824 > > Here, c are the count of the numbers 0,1,2,...,9 in y. > > The maximum absolute difference between the sample cumulative distribution > n%~+/\c and the the theoretical cumulative distribution +/\10$0.1 is: > > >./ | (n%~+/\c) - +/\10$0.1 > 0.000795616 > > The ⍺=0.01 critical value for the Kolmogorov test > <https://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test> is > approximately > > 1.63 % %: n > 0.0028254 > > Therefore, for this one test, y is uniformly distributed with confidence > > 1-⍺=0.99, like ?n⍴10. > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
