[R] Ignoring the domain of RV in punif()
Eric Berger
er|cjberger @end|ng |rom gm@||@com
Tue Oct 23 11:42:02 CEST 2018
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 <hamedhaseli using 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 <ericjberger using 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 <hamedhaseli using 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]]
>>>
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