Ignoring the domain of RV in punif()

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 <hamedhaseli at 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.

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