Probabilities::InverseGaussianCDF Function

Overload List

#SignatureDescription
1double InverseGaussianCDF(double x, double Mu, double Lambda);Inverse Gaussian (Wald) cumulative distribution function (CDF).
2void InverseGaussianCDF(TDenseMtxVec *X, double Mu, double Lambda, TDenseMtxVec *Res);Inverse Gaussian distribution CDF (vectorized).

Overload 1: double InverseGaussianCDF(double x, double Mu, double Lambda);

Inverse Gaussian (Wald) cumulative distribution function (CDF).

#NameTypeDescription
1xdoubleFunction domain, non-negative real value (x>=0).
2MudoubleDistribution mean parameter. Mu must be a positive scalar (Mu>0).
3LambdadoubleDistribution shape parameter. Lambda must be a positive scalar (Lambda>0).

Returns: the inverse Gaussian CDF for value x using parameters Mu (mean) and Lambda (shape), where both are positive. Returns NaN if Mu<=0, Lambda<=0, or x<0.

Remarks:

With Phi the standard normal CDF and erf the error function, the inverse Gaussian CDF is

CDF(x | mu,lambda) = 1/2(1+erf[sqrt(lambda/2x)(x/mu-1)]) + 1/2 e^(2lambda/mu)(1-erf[sqrt(lambda/2x)(x/mu+1)]) .

It is monotone non-decreasing; CDF tends to 0 as x tends to 0+ and to 1 as x tends to +infinity. Returns NaN for x<0, Mu<=0 or Lambda<=0.

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

Overload 2: void InverseGaussianCDF(TDenseMtxVec *X, double Mu, double Lambda, TDenseMtxVec *Res);

Inverse Gaussian distribution CDF (vectorized).

#NameTypeDescription
1XTDenseMtxVec *Defines distribution domain, vector or matrix with positive real values.
2MudoubleDefines distribution Mu parameter. Mu must be a positive scalar.
3LambdadoubleDefines distribution Lambda parameter. Lambda must be a positive scalar.
4ResTDenseMtxVec *After calculation stores the CDF calculated from X, Mu, and Lambda. Length and Complex properties of Res are adjusted automatically to match Length and Complex properties of X.
Declared in Dew::Math::Units::Probabilities · Dew.Math/Units.Probabilities.h · Cross-compiler