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From: Deane Yang (deane_yang_at_[hidden])
Date: 2006-07-12 18:13:45

Topher Cooper wrote:
> At 05:11 AM 7/12/2006, you wrote:
>> 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
> Sorry, as attractive as it seems at first blush, I think just
> "probability" is a very poor choice. ...

<explanation about why and discussion about using intervals snipped>

I definitely do not want to use the same function name for both the
density function and the cumulative probability. Your point about people
confusing the meaning of the density function is on the mark, and I
think using the same function name will only exacerbate the confusion.

Do I would still vote for:

double density(double x) const;

(Despite the origin of the word "density" from physics, it is definitely
used by mathematicians, statisticans, and engineers to mean exactly
this. And I agree that the word "distribution" is not a synonym for

On the other hand, I like the idea of using an interval type for the
"probability" function and requiring an explicit interval constructor
when calling the function, like

student_t dist(2.0);
double p = dist.probability(interval(-1.0, 2.0));
double q = dist.probability(interval(infinity, -1.0));

To me, syntax like this just makes it easier for me to understand what's
going on.

And I agree that we shouldn't just use the Boost Interval library. I
think we should define an interval class specific to the statistics
library, where the left endpoint is allowed to be -infinity and the
right endpoint +infinity.

Then we get a syntax that is easy to read and understand, and we don't
need to come up with a good name for the cumulative or complementary
cumulative probability functions.

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