Cdf.Beta Method

Evaluates the beta cumulative probability distribution function.

public static double Beta(
   double x,
   double pin,
   double qin
);

Parameters

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

Return Value

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

Remarks

Method 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 . 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 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 $\beta_x (p, q)$ .

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

Plot of Beta Distribution Function

Cdf.Beta Method

Parameters

Return Value

Remarks

See Also