Probabilities::FermiDiracPDF Function

Overload List

#SignatureDescription
1double FermiDiracPDF(double x, double Mu, double s);Fermi-Dirac occupation function (PDF form).
2void FermiDiracPDF(TDenseMtxVec *x, double Mu, double s, TDenseMtxVec *y);Fermi-Dirac probability density function (PDF).

Overload 1: double FermiDiracPDF(double x, double Mu, double s);

Fermi-Dirac occupation function (PDF form).

#NameTypeDescription
1xdoubleFunction domain, real value.
2MudoubleLocation (chemical-potential) parameter, real value.
3sdoubleShape parameter, real value.

Returns: the Fermi-Dirac occupation value at x for the given Mu and s. This is NOT a normalized probability density.

Remarks:

Computes the Fermi-Dirac statistical weight that arises in the study of half-integer-spin particles (fermions):

f(x|mu,s)=x^s/(exp(x-mu)+1)

This is the physics occupation form, not a normalized PMF; no parameter validation is performed. Unlike the Bose-Einstein form the denominator never vanishes for real x.

See Also: Probabilities::BoseEinsteinPDF, Probabilities::FermiDiracCDF
Declared in Dew::Math::Units::Probabilities · Dew.Math/Units.Probabilities.h · Cross-compiler

Overload 2: void FermiDiracPDF(TDenseMtxVec *x, double Mu, double s, TDenseMtxVec *y);

Fermi-Dirac probability density function (PDF).

#NameTypeDescription
1xTDenseMtxVec *Function domain, real value.
2MudoubleLocation parameter, real value.
3sdoubleShape parameter, real positive value.
4yTDenseMtxVec *Contains result.

Returns: Fermi-Dirac probability density function (PDF).

Remarks:

Calculates the Fermi-Dirac PDF for x using the parameters Mu and s. The distribution arises in the study of half-integer spin particles in physics. Half-integer spin particles are described by Fermi-Dirac statistics and are called FERMIONS. Fermi-Dirac PDF is defined by the following equation:

PDF(xμ,s)=xsexp(xμ)+1\text{PDF}\left(x| \mu,s\right)= \cfrac{x ^s}{\exp (x-\mu)+1}
See Also: Probabilities::BoseEinsteinPDF
Declared in Dew::Math::Units::Probabilities · Dew.Math/Units.Probabilities.h · Cross-compiler