Evaluates the inverse of 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 p,
	double pin,
	double qin
)
Visual Basic (Declaration)
Public Shared Function Beta ( _
	p As Double, _
	pin As Double, _
	qin As Double _
) As Double
Visual C++
public:
static double Beta(
	double p, 
	double pin, 
	double qin
)

Parameters

p
Type: System..::.Double
A double, the probability for which the inverse of the beta CDF 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 a value less than or equal to this returned value is p.

Remarks

Method InvCdf.Beta evaluates the inverse distribution function of a beta random variable with parameters pin and qin, that is, with P = p, p = pin, and q =qin, it determines x (equal to InvCdf.Beta(p, pin, qin)), such that
P=\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 probability that the random variable takes a value less than or equal to x is P.

See Also