how to use quadrature to integrate some complicated functions

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).

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.

Thanks!

Jeff

--
View this message in context: http://r.789695.n4.nabble.com/how-to-use-quadrature-to-integrate-some-complicated-functions-tp3996765p3996765.html
Sent from the R help mailing list archive at Nabble.com.

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.Shang.5 at 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).

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.