Thanks. The problems you suggested are not a problem for me, because: a. ?y is assumed to be uniformly random for any test. b. m can be as large as I like, and I can keep doing ?p until I get n number which are less than q.
On Thu, Jul 16, 2020 at 11:33 AM Raul Miller <[email protected]> wrote: > Yes, assuming that there's no other dependence on the values appearing > in ?m$p and that the ? in ?m$p is actually uniform. (If there's > artifacts, this process may (or may not) amplify them.) > > Remember of course that there's no guarantee that there will be n > values in ?m$p which are less than q. > > Thanks, > > -- > Raul > > > On Thu, Jul 16, 2020 at 2:29 PM Roger Hui <[email protected]> > wrote: > > > > Arrgh, > > > > Is it valid to generate ?m$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 > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
