Evaluates the beta cumulative probability distribution function.

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

Syntax

C#
public static double Beta(
	double x,
	double pin,
	double qin
)
Visual Basic (Declaration)
Public Shared Function Beta ( _
	x As Double, _
	pin As Double, _
	qin As Double _
) As Double
Visual C++
public:
static double Beta(
	double x, 
	double pin, 
	double qin
)

Parameters

x
Type: System..::.Double
A double, the argument at which the function is to be evaluated.
pin
Type: System..::.Double
A double, the first beta distribution parameter.
qin
Type: System..::.Double
A double, the second beta distribution parameter.

Return Value

A double, the probability that a beta random variable takes on a value less than or equal to x.

Remarks

Method Cdf.Beta evaluates the distribution function of a beta random variable with parameters pin and qin. This function is sometimes called the incomplete beta ratio and, with p = pin and q = qin, is denoted by I_x(p, q). It is given by

I_x\left({p,\,q}\right)=\frac{{ \Gamma\left(p\right)\Gamma\left(q\right)}}{{\Gamma\left({p + q} \right)}}\int_0^x{\,t^{p-1}\left({1-t}\right)^{q-1}dt}

where \Gamma(\cdot) is the gamma function. The value of the distribution function I_x(p, q) is the probability that the random variable takes a value less than or equal to x.

The integral in the expression above is called the incomplete beta function and is denoted by \beta_x(p, q). The constant in the expression is the reciprocal of the beta function (the incomplete function evaluated at one) and is denoted by \beta_1(p, q) .

Cdf.Beta uses the method of Bosten and Battiste (1974).

Plot of Beta Distribution Function

See Also