Re: [boost] [math/staticstics/design] Howbesttonamestatisticalfunctions?

From: John Maddock (john_at_[hidden])
Date: 2006-07-12 12:18:53

Paul A Bristow wrote:
>>  >>  As I mentioned before, these should be member functions,
>>  >>  which could be called "density" (also called 'mass')
>>
>>  Or distribution :-)
>
> This seems quite clear to me - both density and mass sound too
> physical to me,
> though they are in common use.
>
> What is important is that the documentation gives ALL the other
> possible names.

Yep, we'll need a glossary for sure.

>>  >>  The inverse function could be called "inverse_cumulative"
>>  > But excessively long :-(
>>  True, how about "persentile", or is that to ambiguous?
>
> Percentile might be better  - it is in the dictionary ;-))
>
> But quantile is a more modern term and doesn't raise any questions
> about multiplying /dividing by/with 100, a source of unnecessary
> confusion - as we have found with Boost.Test.
>
> So I'm strongly in favour of quantile.

Agreed.

> But I also wonder if 'fraction' is a possible name?

Oh god another one :-)  No lets stick with quantile IMO, and add the other 
to the glossary.

>>  It would also be more natural to me for the
>>  cumulative_probability parameter to come last in the list.
>
> Why?  Quantile is also cumulative?

Actually I'm not sure it matters after all which order they come in :-)

I've just got used to your free functions, where either the form is:

something_inv(random-or-shape-param, P-or-Q-param);

> Which also means that the cost of a Q or complement function is
> nothing unless you use it.
> (and you probably won't use the P version as well).

Right and I think in most cases they're trivial to provide?  If that turns 
out not to be the case drop 'em and see if anyone complains :-)

>>  dist.pdf(x) -- Probability Density Function, this is what looks like
>>  a "bell shaped curve" for a normal distribution, for
>>  example.  A.k.a. "p"
>>  dist.cdf(x) -- Cumulative Distribution Function.  P
>>  dist.ccdf(x) -- Complementary Cumulative Distribution Function;
>>  ccdf(x) = 1 - cdf(x)
>>  dist.icdf(p) -- Inverse Cumulative Distribution Function: P';
>>  icdf(cdf(x)) = x and vice versa
>>  dist.iccdf(p) -- Inverse Complementary Cumulative Distribution
>>  Function; iccdf(p) = icdf(1-p); iccdf(ccdf(x)) = x
>
> My instinct is that these are too abbreviated, despite their
> logicalness.

Agreed.

> But this is the key problem - being clear, not curt, and yet concise.
>
> students_t.inverse_complement_cumulative_probability certains fails!
> ;-))
>
> so we a getting to:
>
> template <T> // T an integral or real or floating-point type.
>
>     T distribution(T x) const; // Probability Density Function or pdf
>     or p T cumulative_probability(T x) const; // Cumulative
> Distribution
> Function.  P
>
> cumulative_probability is too long :-(
>
> Do we REALLY need the cumulative here?
>
>     T probability(T x) const; // Cumulative Distribution Function or
> cdf or
> P

I like probability as a name.

>     T quantile(T probability) const; // Also known as Inverse
> cumulative Distribution Function
>
> what do we call
>
>     T complementary_cumulative_probability(T x) const; //
> Complementary Cumulative Distribution Function.  Q
>
> ??? :-((

How about complementary_probablity ?  Or still too long?

Or probability_c ?

> and worse what about Inverse Complementary Cumulative Distribution
>
> complementary_quantile??? :-((

quantile_c ?

> and the ad hoc 'extra's
>
>     static T degrees_of_freedom(T quantile, T probability) const;
>
> So I feel we haven't QUITE got there yet.

Closer though.

John.