Adding Additional Location and Scale Parameters

In some modelling applications we require a distribution with a specific location and scale: often this equates to a specific mean and standard deviation, although for many distributions the relationship between these properties and the location and scale parameters are non-trivial. See http://www.itl.nist.gov/div898/handbook/eda/section3/eda364.htm for more information.

The obvious way to handle this is via an adapter template:

template <class Dist>
class scaled_distribution
{
   scaled_distribution(
     const Dist dist,
     typename Dist::value_type location,
     typename Dist::value_type scale = 0);
};

Which would then have its own set of overloads for the non-member accessor functions.

An "any_distribution" class

It is easy to add a distribution object that virtualises the actual type of the distribution, and can therefore hold "any" object that conforms to the conceptual requirements of a distribution:

template <class RealType>
class any_distribution
{
public:
   template <class Distribution>
   any_distribution(const Distribution& d);
};

// Get the cdf of the underlying distribution:
template <class RealType>
RealType cdf(const any_distribution<RealType>& d, RealType x);
// etc....

Such a class would facilitate the writing of non-template code that can function with any distribution type.

The Statistical Distribution Explorer utility for Windows is a usage example.

It's not clear yet whether there is a compelling use case though. Possibly tests for goodness of fit might provide such a use case: this needs more investigation.

Higher Level Hypothesis Tests

Higher-level tests roughly corresponding to the Mathematica Hypothesis Tests package could be added reasonably easily, for example:

template <class InputIterator>
typename std::iterator_traits<InputIterator>::value_type
   test_equal_mean(
     InputIterator a,
     InputIterator b,
     typename std::iterator_traits<InputIterator>::value_type expected_mean);

Returns the probability that the data in the sequence [a,b) has the mean expected_mean.

Integration With Statistical Accumulators

Eric Niebler's accumulator framework - also work in progress - provides the means to calculate various statistical properties from experimental data. There is an opportunity to integrate the statistical tests with this framework at some later date:

// Define an accumulator, all required statistics to calculate the test
// are calculated automatically:
accumulator_set<double, features<tag::test_expected_mean> > acc(expected_mean=4);
// Pass our data to the accumulator:
acc = std::for_each(mydata.begin(), mydata.end(), acc);
// Extract the result:
double p = probability(acc);