Re: [boost] [math/staticstics/design] How best tonamestatisticalfunctions?

From: John Maddock (john_at_[hidden])
Date: 2006-07-11 12:26:01

Paul A Bristow wrote:
> What about the Qs? (complements)
>
>>  As I mentioned before, these should be member functions,
>>  which could be called "density" (also called 'mass')

Or distribution :-)

>> and "cumulative".
>
> OHOH many books don't mention either of these words!
>
> The whole nomenclature seems a massive muddle,
> with mathematicians, statistics, and users or all sorts using
> different
> terms
> and everyone thinks they are the 'Standard' :-(
>
> And the highest priority in my book is the END USERS,
> not the professionals.
>
>>  The cumulative density function is a strictly increasing
>>  function and
>>  therefore can be inverted. The inverse function could be called
>>  "inverse_cumulative", which is a completely unambiguous name.
>
> But excessively long :-(

True, how about "persentile", or is that to ambiguous?

>>  Finally, you observe that it is often useful to specify the
>>  cumulative
>>  probability for a given value of the random variable and
>>  solve for the
>>  parameter (the "degrees of freedom" for a Students T
>>  distribution) that
>>  determines the distribution. Since each family of
>>  distributions depends
>>  on a different set of parameters (for example, normal distributions
>>  depend on two parameters, the mean and variance), the
>>  interface for this is trickier to define.
>
>> I can think of two possibilities (I prefer the first):
>>
>>  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;
>
> I don't like 2 either, so I have snipped it ;-)
>
> This seems OK to me.

That could be a static member function, since we're solving for the degrees 
of freedom parameter.  It would also be more natural to me for the 
cumulative_probability parameter to come last in the list.

> I'd be grateful if you could sketch out how you see the whole
> Student's t class would look (just for double and omit the equations
> of course). (This will avoid any confusion about what we are talking
> about).
>
> However:
>
> 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).
> Can anyone advise on this?

For template classes member functions are only instantiated when used, so if 
you only use one member, then that's the only one instantiated.

John.