Evaluates the standard lognormal cumulative probability distribution function.

Namespace: Imsl.Stat
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.0.0

Syntax

C#
public static double LogNormal(
	double x,
	double mu,
	double sigma
)
Visual Basic (Declaration)
Public Shared Function LogNormal ( _
	x As Double, _
	mu As Double, _
	sigma As Double _
) As Double
Visual C++
public:
static double LogNormal(
	double x, 
	double mu, 
	double sigma
)

Parameters

x
Type: System..::.Double
A double scalar value representing the argument at which the function is to be evaluated.
mu
Type: System..::.Double
A double scalar value representing the location parameter.
sigma
Type: System..::.Double
A double scalar value representing the shape parameter. sigma must be a positive.

Return Value

A double scalar value representing the probability that a standard lognormal random variable takes a value less than or equal to x.

Remarks

F\left(x\right)=\frac{1}{x^{\sigma} \sqrt{2\pi}}\int{\frac{1}{t}e^{-\frac{{\ln{t}-\mu}^2}{2{\sigma}^2}} }

Plot of Lognormal Distribution Function

See Also