Probabilities.InverseGaussianCDF Method

Overload List

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

Overload 1: void InverseGaussianCDF(TDenseMtxVec X, Double Mu, Double Lambda, TDenseMtxVec Res)

Inverse Gaussian distribution CDF (vectorized).

#NameDescription
1XDefines distribution domain, vector or matrix with positive real values.
2MuDefines distribution Mu parameter. Mu must be a positive scalar.
3LambdaDefines distribution Lambda parameter. Lambda must be a positive scalar.
4ResAfter 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.

Result: stored in self (calling object)

Overload 2: Double InverseGaussianCDF(Double x, Double Mu, Double Lambda)

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

#NameDescription
1xFunction domain, non-negative real value (x>=0).
2MuDistribution mean parameter. Mu must be a positive scalar (Mu>0).
3LambdaDistribution shape parameter. Lambda must be a positive scalar (Lambda>0).

Returns: Double - 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