R help - Dec 2007 - Numerical precision problem

Dear All,

 

I have a numerical problem:

R, as other statistical software, can tell the difference between very small
numbers and 0, while apparently cannot distinguish a number close to 1 and 1. In
the example below, is it possible to instruct R to recognize that q is different
from 1?
> p=.00000000000000000000000000000001
> p==0
[1] FALSE
> q=.99999999999999999999999999999
> q==1
[1] TRUE

Interestingly, 
> (1-p)==1
[1] TRUE

The main problem I have is that I need to evaluate the inverse of the normal
Cumulative Distribution Function near 1 (but not exactly 1) and the PC cannot
recognize it.

Thank you very much for your help!

Carlo


Please access the attached hyperlink for an important electronic communications
disclaimer: http://www.lse.ac.uk/collections/secretariat/legal/disclaimer.htm

On 21/12/2007 2:52 PM, C.Rosa at lse.ac.uk wrote:
> Dear All,
> 
>  
> 
> I have a numerical problem:
> 
> R, as other statistical software, can tell the difference between very
small numbers and 0, while apparently cannot distinguish a number close to 1 and
1. In the example below, is it possible to instruct R to recognize that q is
different from 1?
No, the limitations are inherent in the floating point representation 
that R uses.
>> p=.00000000000000000000000000000001
> 
>> p==0
> 
> [1] FALSE
> 
>> q=.99999999999999999999999999999
> 
>> q==1
> 
> [1] TRUE
> 
> Interestingly, 
> 
>> (1-p)==1
> 
> [1] TRUE
> 
> The main problem I have is that I need to evaluate the inverse of the
normal Cumulative Distribution Function near 1 (but not exactly 1) and the PC
cannot recognize it.
In this particular case, it's easy:  make use of the symmetry of the 
distribution.  If you want the 1-epsilon quantile of a normal with mean 
mu, find the epsilon quantile, and reflect it through mu:

mu <- 3
-qnorm(1e-30, mean=-mu)

More generally, you can make use of the log.p argument to the quantile 
functions, and the fact that log(1-epsilon) is close to -epsilon:

qnorm(-1e-30, mean=mu, log.p=TRUE)

Duncan Murdoch
> 
> Thank you very much for your help!
> 
> Carlo
> 
> 
> Please access the attached hyperlink for an important electronic
communications disclaimer:
http://www.lse.ac.uk/collections/secretariat/legal/disclaimer.htm
> 
> ______________________________________________
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On Fri, 21 Dec 2007, C.Rosa at lse.ac.uk wrote:
> Dear All,
>
>
>
> I have a numerical problem:
>
> R, as other statistical software, can tell the difference between very 
> small numbers and 0, while apparently cannot distinguish a number close 
> to 1 and 1. In the example below, is it possible to instruct R to 
> recognize that q is different from 1?
No, since q is not different from 1.
>
>> q==1
>
> [1] TRUE
>
>
> The main problem I have is that I need to evaluate the inverse of the 
> normal Cumulative Distribution Function near 1 (but not exactly 1) and 
> the PC cannot recognize it.
>
Use the lower.tail= argument to qnorm (or just use the fact that the 
standard Normal is symmetric)
> p=.00000000000000000000000000000001
> p
[1] 1e-32
> qnorm(p,lower.tail=FALSE)
[1] 11.85613
> -qnorm(p)
[1] 11.85613
>
 	-thomas

C.Rosa at lse.ac.uk wrote:
> Dear All,
> ....
>> (1-p)==1
> 
> [1] TRUE
> 
> The main problem I have is that I need to evaluate the inverse of the
normal Cumulative Distribution Function near 1 (but not exactly 1) and the PC
cannot recognize it.
Evaluate it at 1, evaluate the density at 1, and use basic calculus to 
calculate the differential of the cumulative distribution for small 
differentials away from 1.