Concept definition

template<typename T, typename F, class DeviceType>
concept MC::Distributions::ProbabilityLaw = 
      FloatingPointType<F> && requires(const T& obj, Kokkos::Random_XorShift1024<DeviceType>& gen) {
        { obj.draw(gen) } -> std::same_as<F>;
        { obj.mean() } -> std::same_as<F>;
        { obj.var() } -> std::same_as<F>;
        { obj.skewness() } -> std::same_as<F>;
      }

Detailed Description

Concept for probability distribution laws.

The ProbabilityLaw concept defines the requirements for a type T to model a probability distribution with floating-point computations. It ensures that the type provides methods for drawing random samples and computing common statistical measures such as mean, variance, and skewness.

Template Parameters

T	The type representing a probability distribution.
F	The floating-point type used for computations.
DeviceType	The execution device type for random number generation.

Requirements:

T must support sampling using a Kokkos random number generator.
T must provide methods to compute statistical properties:
- mean(): Returns the expected value (mean) of the distribution.
- var(): Returns the variance of the distribution.
- skewness(): Returns the skewness, measuring asymmetry.

Example usage:

struct NormalDistribution {
    double mean() const { return mu; }
    double var() const { return sigma * sigma; }
    double skewness() const { return 0.0; }
    double draw(Kokkos::Random_XorShift1024<DeviceType>& gen) {return 0.;    }
  };
  static_assert(ProbabilityLaw<NormalDistribution, double, DeviceType>);