[R] Product integral in R

David Winsemius dwinsemius at comcast.net
Sun Dec 18 19:11:27 CET 2011

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.)

David Winsemius, MD
West Hartford, CT

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