PdfNoncentralBeta Method |
Namespace: Imsl.Stat
public static double NoncentralBeta( double x, double shape1, double shape2, double lambda )
The noncentral beta distribution is a generalization of the beta distribution. If is a noncentral chi-square random variable with noncentrality parameter and degrees of freedom, and is a chi-square random variable with degrees of freedom which is statistically independent of , then
is a noncentral beta-distributed random variable and
is a noncentral F-distributed random variable. The PDF for noncentral beta variable X can thus be simply defined in terms of the noncentral F PDF:
where is the noncentral beta PDF with = x, = shape1, = shape2, and noncentrality parameter = lambda; is the noncentral F PDF with argument f, numerator and denominator degrees of freedom and respectively, noncentrality parameter ,
and(See documentation for class Pdf method NoncentralF for a discussion of how the noncentral F PDF is defined and calculated.)
With a noncentrality parameter of zero, the noncentral beta distribution is the same as the beta distribution.