Probabilities::FatigueLifeCDFInv Function

Overload List

#SignatureDescription
1double FatigueLifeCDFInv(double p, double Mu, double gamma, double beta);Fatigue life (Birnbaum-Saunders) percent point function (PPF, quantile / inverse CDF).
2void FatigueLifeCDFInv(TDenseMtxVec *P, double Mu, double gamma, double beta, TDenseMtxVec *Res);Fatigue Life PPF (vectorized).

Overload 1: double FatigueLifeCDFInv(double p, double Mu, double gamma, double beta);

Fatigue life (Birnbaum-Saunders) percent point function (PPF, quantile / inverse CDF).

#NameTypeDescription
1pdoubleProbability, real value on the closed interval [0,1].
2MudoubleDistribution location parameter, real value.
3gammadoubleDistribution shape parameter. gamma must be a positive scalar (gamma>0).
4betadoubleDistribution scale parameter. beta must be a positive scalar (beta>0).

Returns: the value x such that FatigueLifeCDF(x,Mu,gamma,beta)=p. Parameters gamma and beta must be positive and the probability p must lie on [0,1], otherwise the result is NaN.

Remarks:

The inverse CDF has a closed form. Let w=gamma Phi^(-1)(p) where Phi^(-1) is the standard normal quantile; then with z=(x-mu)/beta the relation w=sqrt(z)-sqrt(1/z) inverts to a quadratic in z:

CDFInv(p | mu,gamma,beta) = mu + beta z , z = 1/2( w^2+2 +/- sqrt((w^2+2)^2-4) ) , w=gamma Phi^(-1)(p) .

The "+" root is taken for p>1/2p>1/2 and the "-" root for p<1/2p<1/2. Returns NaN for p outside [0,1], gamma<=0 or beta<=0.

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

Overload 2: void FatigueLifeCDFInv(TDenseMtxVec *P, double Mu, double gamma, double beta, TDenseMtxVec *Res);

Fatigue Life PPF (vectorized).

#NameTypeDescription
1PTDenseMtxVec *Defines distribution probabilities, real vector or matrix with values within closed interval [0,1].
2MudoubleDefines distribution location parameter.
3gammadoubleDefines distribution shape parameter. gamma must be a positive scalar.
4betadoubleDefines distribution scale parameter. beta must be a positive scalar.
5ResTDenseMtxVec *After calculation stores the PPF calculated from P, m, gamma and beta. Length and Complex properties of Res are adjusted automatically to match Length and Complex properties of P.
Declared in Dew::Math::Units::Probabilities · Dew.Math/Units.Probabilities.h · Cross-compiler