[R] Numerical precision problem

[Duncan Murdoch]

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
> 
> 
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