Re: Rounding??

["Andreas J. Guelzow" <aguelzow math concordia ab ca>]

Guenter Milde wrote:

> Ok, we have to admit:  "_never_ worse" is incorrect. 
>
> Still
>
> > There is nothing better about `round towards even'.  
>
>
> is also not true:

And as I said that statement was also compleely unsupported.

> If you have a large sample of random numbers the relative frequency of the
> digits 0 - 9 will be the same. The rounding error for a number with r digits is
> |a - z| <= 0.5e-r, for r = 1 we have 
>  
>  digit round_up even_rule
>   0            0               0
>   1         -1          -1
>   2        -2         -2
>   3        -3         -3
>   4        -4         -4
>   5         5       -5 or 5 (with half/half probability)
>   6         4          4 
>   7         3          3
>   8         2          2
>   9         1          1
>
>
> If we round "the accountants way", the expectation (mean) value of the
> rounding error is 0.5, if we round_to_even, the expectation value of the
> rounding error is 0.

That's correct if we only consider a finite population. We really have a 
continuum of numbers in that interval that are uniformly distributed. In 
that case, which way the single value 0.5000000... is rounded has in 
fact no influence on the integral calculating the expected value.

Andreas

PS: perhaps we should continue this discussion in private

--
Prof. Dr. Andreas J. Guelzow                    
Chair of Science
Concordia University College of Alberta
http://www.math.concordia.ab.ca/aguelzow