Probability.h

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#ifndef _utl_Probability_h_
#define _utl_Probability_h_

#include <utl/Vector.h>
#include <utl/Singleton.h>

#include <TRandom3.h>
#include <TVector3.h>


namespace utl {

  class Probability : public Singleton<Probability> {

  public:
    // optionally set seed of random generator, by default the seed is chosen
    // randomly, so use this option only if you want a reproducible result
    void SetSeed(const unsigned int seed);

    static double GetRayleighPDF(const double x, const double sigma);

    static double GetRayleighCDF(const double x, const double sigma);

    // evaluates the normal pdf with mu and sigma at position x
    static double GetNormalPDF(const double x, const double mu, const double sigma);

    /* Evaluates the von Mises pdf with kappa at position x
     * κ is a measure of concentration (a reciprocal measure of dispersion, so 1/κ is analogous to σ^2).
     * If κ is zero, the distribution is uniform, and for small κ, it is close to uniform.
     * If κ is large, the distribution becomes very concentrated about the angle μ
     * with κ being a measure of the concentration. In fact, as κ increases,
     * the distribution approaches a normal distribution in x  with mean μ and variance 1/κ.
     */
    static long double GetVonMisesPDF(const double x, const double mu, const double kappa);

    // evaluates the Fisher pdf with kappa at position x
    static double GetFisherPDF(const double x, const double kappa);

    // evaluates the Fisher CDF with kappa at position x
    static double GetFisherCDF(const double x, const double kappa);

    double GetRandomRayleigh(const double sigma);

    double GetRandomFisher(const double k);

    utl::Vector GetRandomFisher(const utl::Vector& meanDirection, const double k);

    utl::Vector GetFisher(const utl::Vector& meanDirection, const double alpha);

  private:
    Probability();

    TVector3 GetRandomVectorOnSphere();

    TRandom3 fRand;

    friend class Singleton<Probability>;

  };

}


#endif