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.
