[...]
So either the information is important and then should be placed in the
docs directly, or it's not and then linking to wikipedia is pointless
because the users are not interested in learning all the details about
each distribution function.
What is important is that these distributions can be used from pgbench.
What is a gaussian or an exponential distribution is *not* important as
such.
For me it is not the point of pg documentation to explain probability
theory, but just to provide *precise* information about what is actually
available, for someone who would be interested, without having to read the
source code. At least that is the idea behind the current documentation.
Firstly, it'd be nice if we could add some figures illustrating the
distributions - much better than explaining the shapes in text. I
don't know if we include figures in the existing docs (probably not),
but generating the figures is rather simple.
There is basically no figures in the documentation. Too bad, but it is
understandable: what should be the format (svg, jpg, png, ...), should
it be generated (gnuplot, others), what is the impact on the
documentation build (html, epub, pdf, ...), how portable should it be,
what about compressed formats vs git diffs?
Once you start asking these questions you understand why there are no
figures:-)
I don't see why diffs would be a problem.
I was not only thinking of mathematical figures, I was also thinking of
graphics, some format may be zip containing XML stuff for instance.
Probably nitpicking, but left/right of what? I assume the normal
distribution is placed at 0, so it's left/right of zero.
No, it is around the middle of the interval.
You mean [min,max] interval?
Yep.
I believe the transformation
2.0 * threshold * (i - min - mu + 0.5) / (max - min + 1)
essentially moves the mean into 0, scales the data to [0,1] and then applies
the threshold.
Probably:-) I wrote that some time ago, and it is 10 pm for me:-).
In other words, the general shape of the curve will be exactly the same no
matter the actual min/max (except that for longer intervals the values will
be lower, as there are more possible values).
I don't really see how it's related to this?
[(max-min)/2 - thresholds, (max-min)/2 + threshold]
The gaussian distribution is about reals, but it is used for integers, so
there is a projection on integers from the real values. The function
should compute the probability of drawing a given integer "i" in the
interval, that is given min, max and threshold, what is the probability of
drawing i.
Could we simplify the equation a bit? It's needlessly difficult to
realize it's actually just CDF(i+0.5) - CDF(i-0.5). I think it'd be
good to first define the CDF and then just use that.
ISTM that PHI is *the* normal CDF, which is more or less available as
such in various environment (matlab, python, excel...). Well, why not
defined the particular CDF and use it. Not sure the text would be that
much lighter, though.
PHI is the CDF of the normal distribution, not the modified probability
distribution here (with threshold and scaled to the desired interval).
Yep, that is exactly what I was saying, I think.
This seems broken - too many sentences about the 67% and 95%.
The point is to provide rules of thumb to describe how the distribution
is shaped. Any better sentence is welcome.
Ah, I misread the sentence initially. I haven't realized it speaks about
1/threshold in the first part, and the second part is an example for
threshold=4.0. So I thought it's a repetition of the first part.
Maybe it needs spacing and colons and rewording, if it too hard to parse.
Does it make sense to explicitly mention the implementation detail
(Box-Muller transform) here?
No, my point was exactly the opposite - removing the mention of Box-Muller
entirely, not adding more details about it.
Ok. I think that the fact that it relies on the Box-Muller transform is
relevant, because there are other methods to generate a gaussian
distribution, and I would say that there is no reason to have to go to the
source code to check that. But I would not provide further details. So I'm
fine with the current status.
--
Fabien.
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