R help - Jul 2006 - workaround for numeric problems

Dear R-people,

I have to compute 

C - -(pnorm(B)*dnorm(B)*B + dnorm(B)^2)/pnorm(B)^2

This expression seems to be converging to -1 if B approaches to -Inf
(although I am unable to prove it).  R has no problems until B equals
around -28 or less, where both numerator and denominator go to 0 and
you get NaN. A simple workaround I did was

C <- ifelse(B > -25,
           -(pnorm(B)*dnorm(B)*B + dnorm(B)^2)/pnorm(B)^2,
            -1)

It works well for me (32bit intel/linux platform).  But what about
other processors/platforms/compilator options?  Are there any better
ways for finding out at which values the numerical problems start?
Can one derive something from .Machine$double.eps (but what about the
precison of dnorm and other analytic functions)?

Thanks in advance,
Ott

I'd compute this in the log-scale (taking also advantage of the
'log'
and 'log.p' arguments of dnorm() and pnorm(), respectively), and then 
transform back, e.g.,

fn1 <- function(B){
    -(pnorm(B) * dnorm(B) * B + dnorm(B)^2)/pnorm(B)^2
}

fn2 <- function(B){
    p1 <- dnorm(B, log = TRUE) + log(-B) - pnorm(B, log.p = TRUE)
    p2 <- 2 * (dnorm(B, log = TRUE) - pnorm(B, log.p = TRUE))
    exp(p1) - exp(p2)
}

fn1(c(-15, -25, -35, -55, -105))
fn2(c(-15, -25, -35, -55, -105))


I hope it helps.

Best,
Dimitris

---- 
Dimitris Rizopoulos
Ph.D. Student
Biostatistical Centre
School of Public Health
Catholic University of Leuven

Address: Kapucijnenvoer 35, Leuven, Belgium
Tel: +32/(0)16/336899
Fax: +32/(0)16/337015
Web: http://med.kuleuven.be/biostat/
     http://www.student.kuleuven.be/~m0390867/dimitris.htm


Quoting Ott Toomet <otoomet at ut.ee>:
> Dear R-people,
> 
> I have to compute 
> 
> C - -(pnorm(B)*dnorm(B)*B + dnorm(B)^2)/pnorm(B)^2
> 
> This expression seems to be converging to -1 if B approaches to -Inf
> (although I am unable to prove it).  R has no problems until B
> equals
> around -28 or less, where both numerator and denominator go to 0 and
> you get NaN. A simple workaround I did was
> 
> C <- ifelse(B > -25,
>            -(pnorm(B)*dnorm(B)*B + dnorm(B)^2)/pnorm(B)^2,
>             -1)
> 
> It works well for me (32bit intel/linux platform).  But what about
> other processors/platforms/compilator options?  Are there any better
> ways for finding out at which values the numerical problems start?
> Can one derive something from .Machine$double.eps (but what about
> the
> precison of dnorm and other analytic functions)?
> 
> Thanks in advance,
> Ott
> 
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