The domain of definition is 0 <= x <= 1. In this
implementation a and b are restricted to positive values.
The integral from x to 1 may be obtained by the symmetry
relation
betaDistributionCompl(a, b, x ) = betaDistribution( b, a, 1-x )
The integral is evaluated by a continued fraction expansion
or, when b*x is small, by a power series.
The inverse finds the value of x for which betaDistribution(a,b,x) - y = 0
Beta distribution and its inverse
Returns the incomplete beta integral of the arguments, evaluated from zero to x. The function is defined as
betaDistribution = Γ(a+b)/(Γ(a) Γ(b)) * $(INTEGRATE 0, x) ta-1(1-t)b-1 dt
The domain of definition is 0 <= x <= 1. In this implementation a and b are restricted to positive values. The integral from x to 1 may be obtained by the symmetry relation
betaDistributionCompl(a, b, x ) = betaDistribution( b, a, 1-x )
The integral is evaluated by a continued fraction expansion or, when b*x is small, by a power series.
The inverse finds the value of x for which betaDistribution(a,b,x) - y = 0