On Thu, Mar 22, 2012 at 04:17:20PM -0700, casperyc wrote:
> Hi all,
> myint=function(mu,sigma){
> integrate(function(x) dnorm(x,mu,sigma)/(1+exp(-x)),-Inf,Inf)$value
> }
>
> mymu=seq(-3,3,length(1000))
> mysigma=seq(0,1,length(500))[-1]
>
> k=1
> v=c()
> for (j in 1:length(mymu)) {
> for (i in 1:length(mysigma)) {
> v[k]=myint(mymu[j],mysigma[i])
> k=k+1
> }
> }
>
>
> Basically, I want to investigate for what values of mu and sigma, the
> integral is divergent.
Hi.
The function dnorm(x,mu,sigma)/(1+exp(-x)) has a finite integral
over (-Inf, Inf) for every mu, sigma. The reason is that
dnorm(x,mu,sigma)
is nonnegative and
0 < 1/(1+exp(-x)) < 1
So, the integral of dnorm(x,mu,sigma)/(1+exp(-x)) is upper bounded
by the integral of dnorm(x,mu,sigma), which is 1.
Hope this helps.
Petr Savicky.
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