Cdf.LogNormal Method

CdfLogNormal Method

Evaluates the standard lognormal cumulative probability distribution function.

Namespace: Imsl.Stat
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0

Syntax

public static double LogNormal(
	double x,
	double mu,
	double sigma
)

Public Shared Function LogNormal ( 
	x As Double,
	mu As Double,
	sigma As Double
) As Double

public:
static double LogNormal(
	double x, 
	double mu, 
	double sigma
)

static member LogNormal : 
        x : float * 
        mu : float * 
        sigma : float -> float

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

Type: Double
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