R help - Aug 2010 - Need help to understand integrate function

Hi,

I'm running into a wall when trying to use the integrate function. I
have the following setting:

powerLaw2 <- function(x,l1,l2,c0,t0) {

   idx <- which(x <= 0);
   if (length(idx) > 0) {
      x[idx] <- 0;
   }

   xl <- (-l1+l2)*log(x/t0);
   L <- log(c0)-l1*log(x)-log(1+exp(xl));
   L <- exp(L);
   return(L);
}

plCDF2 <- function(x,l1,l2,c0,t0) {

   print(c(l1,l2,c0,t0));
   cdf <-
integrate(f=powerLaw2,lower=x,upper=Inf,l1=l1,l2=l2,c0=c0,t0=t0,stop.on.error=T);
   return(cdf$value);

}

I know that as long as my l1 > 1 and l2 < 1 the integration above
should converge. However, this doesn't seem to be the case when I call
integrate function with the following parameter:


Browse[1]>
integrate(f=powerLaw2,lower=1e-09,upper=Inf,l1=1.8980185,l2=-0.0804259,c0=1,t0=259.78,stop.on.error=T)
failed with message 'the integral is probably divergent'

Would you please shed some light? And how could I prevent this
situation? Thank you.

Rgds,

Rob

Try this:

options(digits=10)
> integrate(f=powerLaw2, lower=0, upper=Inf, l1=1.8980185, l2=-0.0804259,
c0=1, t0=259.78, rel.tol=1.e-10)
0.01089019946 with absolute error < 3.7e-11


Ravi.
____________________________________________________________________

Ravi Varadhan, Ph.D.
Assistant Professor,
Division of Geriatric Medicine and Gerontology
School of Medicine
Johns Hopkins University

Ph. (410) 502-2619
email: rvaradhan at jhmi.edu


----- Original Message -----
From: R_help Help <rhelpacc at gmail.com>
Date: Wednesday, August 11, 2010 9:44 pm
Subject: [R] Need help to understand integrate function
To: r-help at r-project.org

> Hi,
>  
>  I'm running into a wall when trying to use the integrate function. I
>  have the following setting:
>  
>  powerLaw2 <- function(x,l1,l2,c0,t0) {
>  
>     idx <- which(x <= 0);
>     if (length(idx) > 0) {
>        x[idx] <- 0;
>     }
>  
>     xl <- (-l1+l2)*log(x/t0);
>     L <- log(c0)-l1*log(x)-log(1+exp(xl));
>     L <- exp(L);
>     return(L);
>  }
>  
>  plCDF2 <- function(x,l1,l2,c0,t0) {
>  
>     print(c(l1,l2,c0,t0));
>     cdf <-
integrate(f=powerLaw2,lower=x,upper=Inf,l1=l1,l2=l2,c0=c0,t0=t0,stop.on.error=T);
>     return(cdf$value);
>  
>  }
>  
>  I know that as long as my l1 > 1 and l2 < 1 the integration above
>  should converge. However, this doesn't seem to be the case when I call
>  integrate function with the following parameter:
>  
>  
>  Browse[1]>
integrate(f=powerLaw2,lower=1e-09,upper=Inf,l1=1.8980185,l2=-0.0804259,c0=1,t0=259.78,stop.on.error=T)
>  failed with message 'the integral is probably divergent'
>  
>  Would you please shed some light? And how could I prevent this
>  situation? Thank you.
>  
>  Rgds,
>  
>  Rob
>  
>  ______________________________________________
>  R-help at r-project.org mailing list
>  
>  PLEASE do read the posting guide 
>  and provide commented, minimal, self-contained, reproducible code.