Re: [boost] [math/staticstics/design] How best to name statistical functions?

From: Deane Yang (deane_yang_at_[hidden])
Date: 2006-07-10 16:40:56

Paul A Bristow wrote:
> |  -----Original Message-----
> |  From:  Kevin Lynch

> |  Why not hide the functions behind a class interface?  After all, the
> |  various functions are "properties" of the distributions.  Hence:
> |  
> |  class students_t {
> |  	students_t(double mu);
> |  	double P(double x);
> |  	double Q(double x);
> |  	double invP(double p); (or perhaps inverseP or Pinv or 
> |  something)
> |  	.....
> |  }
> |  
> |  class normal {
> |  	normal(double mu, double sigma);
> |  	double P(double x);
> |  	double Q(double x);
> |  	double invP(double x);
> |  	......
> |  }
> 
> Rather interesting idea.

I support Kevin's proposal rather strongly for exactly the reasons he 
states. But I'm not sure what P, Q, invP mean. I would prefer:

double density(double x);
double cumulative(double x);
double inverse_cumulative(double y);

> How would you envisage this working with Fisher, for example which has
> degrees of freedom 1 and 2, and a variance ratio.
> 
> Is this a 1D or 2D or 3D?
> 
> Its inversion will return df1 (given df2 and F and Probability)
> or df2 (given df1, F and Prob)
> or F (given Df1 and df2 and Prob)
> 
> WOuld you like to flesh out how you suggest handling all these?
> 

Could you clarify your question? Isn't the F distribution still the 
probability distribution of a single real random variable? The 
cumulative and inverse cumulative density functions have a consistent 
mathematical meaning for any 1-dimensional probability distribution, do 
they not?