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.