On Nov 8, 2011, at 9:43 AM, R. Michael Weylandt wrote:
Have you tried wrapping it in a function and using integrate()? R is
pretty good at handling numerical integration. If integrate() isn't
good for you, can you say more as to why?
Michael
On Nov 6, 2011, at 4:15 PM, JeffND <zuofeng.shan...@nd.edu> wrote:
Hello to all,
I am having trouble with intregrating a complicated uni-dimensional
function
of the following form
Phi(x-a_1)*Phi(x-a_2)*...*Phi(x-a_{n-1})*phi(x-a_n).
Here n is about 5000, Phi is the cumulative distribution function of
standard normal,
phi is the density function of standard normal, and x ranges over
(-infty,infty).
The density of a standard normal is very tractable mathematically. Why
wouldn't you extract the arguments and sum them before submitting to
integration ... which also might not be needed since pnorm could
economically provide the answer. Perhaps with limits a, b:
suitable_norm_factor*
pnorm(
dnorm( sum(x-a_1, x-a_2, ..., x-a_{n-1}, x-a_n) ), a,
lower.tail=FALSE) ) -
pnorm(
dnorm( sum(x-a_1, x-a_2, ..., x-a_{n-1}, x-a_n) ), b,
lower.tail=FALSE) ) )
My idea is to to use quadrature to handle this integral. But since
Phi has
not cloaed form,
I don't know how to do this effeciently. I appreciate very much if
someone
has any ideas about it.
If efficiency is desired ... use mathematical theory to maximum extent
before resorting to pickaxes.
--
David Winsemius, MD
West Hartford, CT
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