gschmitt@i50s8.ira.uka.de (G.Schmitt) (03/08/91)
BINS BUG in Revision D ROM
The "bug" (if it really is one, but to me it seems so) I want to describe here has
probably been announced before. It concerns the BINS algorithm on page 2 of the STATISTIC menu. I noticed the error doing some statistic stuff with measurement data. The easiest way to explain is to give a short example showing the same error effect.
Consider the folowing example:
Create a statistical matrix (which is a vector in this special case) containing only the
5 integer values
1 2 3 4 5 .
Now try the following argument sequence for BINS:
2 as the minimal x-value in level 3
1 as the class width in level 2
3 as the number of classes you want in level 1.
This means a division into 3 classes:
1 | 2 | 3 | 4 | 5
lower outside 3 classes with 1 value each upper outside value.
value
Performing the BINS routine now yields the two vectors (a matrix and a vector)
[ [1] [1] [2] ] the class frequencies and
[1 0] the frequencies outside, which is not the correct result I think.
I expected the following as the correct result:
[ [1] [1] [1] ] and
[1 1].
The problem always arises if the first upper outside value (the value 5 in the former example) lies on the edge of the last class (the effect is independent of class width of course). A repetition of the above example with the slight modification of writing the integer value 6 instead of the 5 in the statistical matrix gives the correct result
[ [1] [1] [1] ] and
[1 1].
The bug (if it really is one; what says the statistic expert?) is easy to fix.
Repeating the example with the first statistical matrix, which showed the error effect
(1 2 3 4 5) but with the following parameters for BINS:
1.5 (or any other value near but smaller than 2, the originally intended minimal x-value)
1 as class width
3 as the number of classes
yields the correct result.
The above handling also works with non integer values of course, as long as the numbers you
deal with, don`t claim the full fractional range of the HP for their representation.
Would be interesting to hear from a REV E owner, whether or not the same effect occurs on his machine.
Gerarddianab@hpcvra.cv.hp.com. (Diana Byrne) (03/12/91)
BINS was designed to treat the interval from xmin to xmax on the real
number line as a CLOSED interval (where xmax = xmin + width * N).
Thus, it divides the interval into N-1 half-open intervals of the form
{x : xi <= x < xi+width} and 1 closed interval {x : xmax-width <= x <= xmax}.
xmax is included in the last interval.
Your example can be depicted as follows:
[----)[----)[----]
1 2 3 4 5
xmin xmax
xmin=2, width=1, N=3, xmax=5, there is one value (1) which is less than xmin
and no values which are greater than xmax.