Yes, now it makes more sense. Okay, I think that I am convinced and we can close this ticket.
Thanks Eric. Regards, Hamed. On Tue, 23 Oct 2018 at 10:42, Eric Berger <ericjber...@gmail.com> wrote: > Hi Hamed, > That reference is sloppy. Try looking at > https://en.wikipedia.org/wiki/Cumulative_distribution_function > and in particular the first example which deals with a Unif[0,1] r.v. > > Best, > Eric > > > On Tue, Oct 23, 2018 at 12:35 PM Hamed Ha <hamedhas...@gmail.com> wrote: > >> Hi Eric, >> >> Thank you for your reply. >> >> I should say that your justification makes sense to me. However, I am in >> doubt that CDF defines by the Pr(x <= X) for all X? that is the domain of >> RV is totally ignored in the definition. >> >> It makes a conflict between the formula and the theoretical definition. >> >> Please see page 115 in >> >> https://books.google.co.uk/books?id=FEE8D1tRl30C&printsec=frontcover&dq=statistical+distribution&hl=en&sa=X&ved=0ahUKEwjp3PGZmJzeAhUQqxoKHV7OBJgQ6AEIKTAA#v=onepage&q=uniform&f=false >> The >> >> >> Thanks. >> Hamed. >> >> >> >> On Tue, 23 Oct 2018 at 10:21, Eric Berger <ericjber...@gmail.com> wrote: >> >>> Hi Hamed, >>> I disagree with your criticism. >>> For a random variable X >>> X: D - - - > R >>> its CDF F is defined by >>> F: R - - - > [0,1] >>> F(z) = Prob(X <= z) >>> >>> The fact that you wrote a convenient formula for the CDF >>> F(z) = (z-a)/(b-a) a <= z <= b >>> in a particular range for z is your decision, and as you noted this >>> formula will give the wrong value for z outside the interval [a,b]. >>> But the problem lies in your formula, not the definition of the CDF >>> which would be, in your case: >>> >>> F(z) = 0 if z <= a >>> = (z-a)/(b-a) if a <= z <= b >>> = 1 if 1 <= z >>> >>> HTH, >>> Eric >>> >>> >>> >>> >>> On Tue, Oct 23, 2018 at 12:05 PM Hamed Ha <hamedhas...@gmail.com> wrote: >>> >>>> Hi All, >>>> >>>> I recently discovered an interesting issue with the punif() function. >>>> Let >>>> X~Uiform[a,b] then the CDF is defined by F(x)=(x-a)/(b-a) for (a<= x<= >>>> b). >>>> The important fact here is the domain of the random variable X. Having >>>> said >>>> that, R returns CDF for any value in the real domain. >>>> >>>> I understand that one can justify this by extending the domain of X and >>>> assigning zero probabilities to the values outside the domain. However, >>>> theoretically, it is not true to return a value for the CDF outside the >>>> domain. Then I propose a patch to R function punif() to return an error >>>> in >>>> this situations. >>>> >>>> Example: >>>> > punif(10^10) >>>> [1] 1 >>>> >>>> >>>> Regards, >>>> Hamed. >>>> >>>> [[alternative HTML version deleted]] >>>> >>>> ______________________________________________ >>>> R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see >>>> https://stat.ethz.ch/mailman/listinfo/r-help >>>> PLEASE do read the posting guide >>>> http://www.R-project.org/posting-guide.html >>>> and provide commented, minimal, self-contained, reproducible code. >>>> >>> [[alternative HTML version deleted]] ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
