IMSL C# Numerical Library

Cdf.LogNormal Method

Evaluates the standard lognormal cumulative probability distribution function.

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

Parameters

x: A double scalar value representing the argument at which the function is to be evaluated.
mu: A double scalar value representing the location parameter.
sigma: 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

Cdf Class | Imsl.Stat Namespace