Re: Rounding??

Guenter Milde wrote:

Ok, we have to admit: "_never_ worse" is incorrect.

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.


PS: perhaps we should continue this discussion in private

Prof. Dr. Andreas J. Guelzow Chair of Science
Concordia University College of Alberta

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