Re: [boost] [math/staticstics/design] How besttonamestatisticalfunctions?

From: Paul A Bristow (pbristow_at_[hidden])
Date: 2006-07-12 05:11:24

|  -----Original Message-----
|  From: boost-bounces_at_[hidden] 
|  [mailto:boost-bounces_at_[hidden]] On Behalf Of John Maddock
|  Sent: 11 July 2006 17:26
|  To: boost_at_[hidden]
|  Subject: Re: [boost] [math/staticstics/design] How 
|  besttonamestatisticalfunctions?
|  
|  >>  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.

|  >>  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.

But I also wonder if 'fraction' is a possible name?
 
|  >>  1) Define ad hoc inverse functions for each specific
|  >>  distribution. So
|  >>  for the Students T distribution, you would define a member
|  >>  function of the form:
|  >>
|  >>  double degrees_of_freedom(double cumulative_probability, double
|  >> random_variable) const;
|  
|  That could be a static member function, since we're solving 
|  for the degrees of freedom parameter.

OK

|  It would also be more natural to me for the 
|  cumulative_probability parameter to come last in the list.

Why?  Quantile is also cumulative?

|  > But I still worried that the whole scheme will lead to much bigger
|  > code compared to a set of names of (template) functions
|  > (because code that isn't in fact used will be generated).
|  
|  For template classes member functions are only instantiated 
|  when used, so if 
|  you only use one member, then that's the only one instantiated.

What that's what I thought - but I wanted expert reassurance before driving
into a dead-end ;-)

So my worry turns into a killer feature - keeping the cost of calling a
single student's t down to reasonable levels is crucially important.

Compared to linking to a "All_the_stats_functions_you_could_ever_want'.dll
it should be easily 'affordable', as they say.

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).

>>  In other words, 1 - P. Right? One response is why do you
>>  need to define
>>  it, given how easy it is to get from the cumulative density
>> function?
> Perhaps not really needed? Is there an accuracy reason for both?

| It depends how accurate you want to be: calculating 1-P incurs
cancellation 
| error if P is very near 1, where as for most (all?) distributions we can 
| calculate Q directly without the subraction from unity.

| I think the "Boostified" name would be in all lower case: students_t or
whatever.

Agree with this.

Paul

---
Paul A Bristow
Prizet Farmhouse, Kendal, Cumbria UK LA8 8AB
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