Product integral in R
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