Cdf.Pareto Method

CdfPareto Method

Evaluates the Pareto cumulative probability distribution function.

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

Syntax

public static double Pareto(
	double x,
	double xm,
	double k
)

Public Shared Function Pareto ( 
	x As Double,
	xm As Double,
	k As Double
) As Double

public:
static double Pareto(
	double x, 
	double xm, 
	double k
)

static member Pareto : 
        x : float * 
        xm : float * 
        k : float -> float

x: Type: SystemDouble
A double scalar value representing the argument at which the function is to be evaluated.
xm: Type: SystemDouble
A double scalar value representing the scale parameter, .
k: Type: SystemDouble
A double scalar value representing the shape parameter, .

Type: Double
A double scalar value representing the probability that a Pareto random variable takes a value less than or equal to x.

Remarks

Method Cdf.Pareto evaluates the distribution function, F, of a Pareto random variable with scale parameter

and shape parameter k. It is given by

$F(x,x_m,k)=1-\left(\frac{x_m}{x}\right)^{ k}$

where

and

. The function is only defined for $x\geq x_m$ .