Overload List
| # | Signature | Description |
|---|---|---|
| 1 | void InverseGaussianCDF(TDenseMtxVec X, Double Mu, Double Lambda, TDenseMtxVec Res) | Inverse Gaussian distribution CDF (vectorized). |
| 2 | Double 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).
| # | Name | Description |
|---|---|---|
| 1 | X | Defines distribution domain, vector or matrix with positive real values. |
| 2 | Mu | Defines distribution Mu parameter. Mu must be a positive scalar. |
| 3 | Lambda | Defines distribution Lambda parameter. Lambda must be a positive scalar. |
| 4 | Res | 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. |
Result: stored in self (calling object)
Overload 2: Double InverseGaussianCDF(Double x, Double Mu, Double Lambda)
Inverse Gaussian (Wald) cumulative distribution function (CDF).
| # | Name | Description |
|---|---|---|
| 1 | x | Function domain, non-negative real value (x>=0). |
| 2 | Mu | Distribution mean parameter. Mu must be a positive scalar (Mu>0). |
| 3 | Lambda | Distribution 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.