Overload List
| # | Signature | Description |
|---|---|---|
| 1 | procedure FatigueLifePDF(const X: TDenseMtxVec; Mu: Double; gamma: Double; beta: Double; const Res: TDenseMtxVec); | Fatigue Life PDF (vectorized). |
| 2 | function FatigueLifePDF(x: Double; Mu: Double; gamma: Double; beta: Double): Double; | Fatigue life (Birnbaum-Saunders) probability density function (PDF). |
Overload 1: procedure FatigueLifePDF(const X: TDenseMtxVec; Mu: Double; gamma: Double; beta: Double; const Res: TDenseMtxVec);
Fatigue Life PDF (vectorized).
| # | Name | Description |
|---|---|---|
| 1 | X | Defines distribution domain, real vector or matrix with real values on open interval (Mu,INF). |
| 2 | Mu | Defines distribution location parameter. |
| 3 | gamma | Defines distribution shape parameter. gamma must be a positive scalar. |
| 4 | beta | Defines distribution scale parameter. beta must be a positive scalar. |
| 5 | Res | After calculation stores the PDF calculated from X, Mu, gamma and beta. 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: function FatigueLifePDF(x: Double; Mu: Double; gamma: Double; beta: Double): Double;
Fatigue life (Birnbaum-Saunders) probability density function (PDF).
| # | Name | Description |
|---|---|---|
| 1 | x | Distribution domain, real value on the open interval (Mu, +Inf). |
| 2 | Mu | Distribution location parameter, real value. |
| 3 | gamma | Distribution shape parameter. gamma must be a positive scalar (gamma>0). |
| 4 | beta | Distribution scale parameter. beta must be a positive scalar (beta>0). |
Returns: Double - the Fatigue life probability density function (PDF) evaluated at x using the location parameter Mu and the positive shape (gamma) and scale (beta) parameters. Returns NaN if gamma<=0, beta<=0, or x<=Mu.
The fatigue life distribution is also known as the Birnbaum-Saunders distribution. Several alternative formulations appear in the literature. With z=(x-mu)/beta and phi the standard normal PDF, the textbook Birnbaum-Saunders density is
PDF(x | mu,gamma,beta) = ((sqrt(z)+sqrt(1/z))/(2gamma(x-mu))) phi((sqrt(z)-sqrt(1/z))/gamma) , z=(x-mu)/beta, x>mu .
NOTE (implementation): the current source evaluates the standard-normal-PDF argument as bigl(z^2-sqrt(1/z)bigr)/gamma instead of bigl(sqrt(z)-sqrt(1/z)bigr)/gamma, so the returned PDF is not the exact derivative of FatigueLifeCDF away from x=mu+beta. Returns NaN for x<=Mu, gamma<=0 or beta<=0.