# Re: [R] Problems with integrate

From: Gabor Grothendieck <ggrothendieck_at_gmail.com>
Date: Sun 11 Dec 2005 - 04:58:04 EST

integrate returns a list, not just the value. Try integrate(...)\$value See ?integrate for details.

On 12/10/05, Tolga Uzuner <tolga@coubros.com> wrote:
> Hi,
>
> Having a weird problem with the integrate function.
>
> I have a function which calculates a loss density: I'd like to integrate
> it to get the distribution.
>
> The loss density function is:
>
> lossdensity<-function(p,Beta,R=0.4){
> # the second derivative of the PDF
> # p is the default probability of the pool at which we are evaluating
> the lossdensity
> # Beta is the correlation with the market factor as a function of K
> # R is the recovery rate
> K=p
> C=qnorm(p) # default threshold for the pool
> A=1/Beta(K)*(C-sqrt(1-Beta(K)^2)*qnorm(K/(1-R)))
> B=qnorm(K/(1-R))
> alpha0=dnorm(A)*sqrt(1-Beta(K)^2)/(dnorm(B)*Beta(K)*(1-R))
> alpha10=-2*dnorm(A)*(C*Beta(K)-A)/(Beta(K)*(1-Beta(K)^2))
> alpha11=(1-R)*dnorm(A)*dnorm(B)*(Beta(K)-A/Beta(K)*(C*Beta(K)-A))/((1-Beta(K)^2)^1.5)
> alpha20=(1-R)*dnorm(A)*dnorm(B)/sqrt(1-Beta(K)^2)
> return(alpha0+(alpha10+alpha11*fd(K,Beta))*fd(K,Beta)+alpha20*fd2(K,Beta))
> }
>
> Beta needs to be passed in as a function:
>
> Beta<-splinefun(c(.03,.06,.09,.12,.22,.6),c(.117,.248,.35,.426,.603,1),method="natural")
>
> Now, when I try out lossdensity, it works fine:
>
> > lossdensity(.02,Beta,.4)
>  0.1444915
>
> I defined lossdistribution as:
>
> lossdistribution<-function(p,Beta,R=0.4){
> integrate(function(x)lossdensity(x,Beta,R),0.0000000000001,p)}
>
>
> But this gives a weird error:
>
> > lossdistribution(0.1,Beta)
> Error in "[<-"(`*tmp*`, k, i, value = c(4.29850518211428, 0, 0, 0, 0, :
> number of items to replace is not a multiple of replacement length
>
>
> What's interesting is, if I use the area function from library(MASS), it
> works:
>
> > lossdistribution<-function(p,Beta,R=0.4){
> + area(function(x){lossdensity(x,Beta,R)},0.00001,p)}
> > lossdistribution(.02,Beta,.4)
>  0.0002177284
>
>
> I could just go ahead and use that, but would like to understand why
> integrate is not working.
>
> Tolga
>
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