# [R] Product integral in R

David Winsemius dwinsemius at comcast.net
Sun Dec 18 19:27:46 CET 2011

On Dec 18, 2011, at 1:11 PM, David Winsemius wrote:

>
> On Dec 18, 2011, at 12:59 PM, Robert A'gata wrote:
>
>> Hi,
>>
>> I am wondering if anybody ever come across any implementation of
>> product integral in R? As far as I googled, I haven't come across any
>> package. Is there any? Thank you.
>>
>> http://en.wikipedia.org/wiki/Product_integral
>
> Survival analysis is essentially an inferential application of
> product integrals. Note the similarity of the third expression
> labeled "Type 1":
>
>        =\exp\left(\int_a^b \ln f(x) \, dx\right)
>
> ... to the definition of the survival function in continuous time
> (different only in the sign of the argument). (And the Kaplan-Meier
> function is a discrete time product integral.)

And the other core statistical notion of likelihood is really a
product integral as well. It is usually handled by taking logs which
turns it into a regular integration problem (and that strategy is
alluded to on the Wikipdia page you cited.) The number of R packages
that do estimation of parameters by maximization of likelihoods must
be very large.

--

David Winsemius, MD
West Hartford, CT