[R] Integration with an Indicator Function in R

[Uwe Ligges]

On 17.02.2011 22:10, li li wrote:
> Hi all,
>     I have some some problem with regard to finding the integral of a
> function containing an indicator function.
> please see the code below:
>
> func1<- function(x, mu){
>    (mu^2)*dnorm(x, mean = mu, sd = 1)*dgamma(x, shape=2)}
> m1star<- function(x){
>     integrate(func1, lower = 0, upper = Inf,x)$val}
> T<- function(x){
>     0.3*dnorm(x)/(0.3*dnorm(x)+0.7*m1star(x))}
>
> func2<- function(x,c){(T(x)<=c)*0.3*dnorm(x)}
> func3<- function(x,c){(T(x)<= c)*(0.3*dnorm(x)+0.7*m1star(x))}
> numer<- function(c){
>     integrate(func2, -Inf, Inf, c)$val}
>
> denom<- function(c){
>     integrate(func3, lower, Inf,c)$val}
>
>
>
> The error message is as below :
>
>> numer(0.5)
> Error in integrate(func1, lower = 0, upper = Inf, x) :
>    the integral is probably divergent


Several problems:

1. Your m1star does not work vectorized which is required here.
This can be fixed by changing the function as follows:

m1star <- function(x){
     sapply(x, function(x) integrate(func1, lower = 0, upper = Inf, x = 
x)$val)
}

2. You will find that func2 calculates T(x). Note that T(x) is not 
undefined for x=0.

I have not investigated further, but my guess is that your problem needs 
some rethinking ...

Best,
Uwe Ligges



>
>
> Thank you very much!
>     Hannah
>
> 	[[alternative HTML version deleted]]
>
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