betaIncomplete

Regularized incomplete beta function Ix(a,b)

Mathematically, if a and b are positive real numbers, and 0 $(LE) x $(LE) 1, then Ix(a,b) = $(INTEGRATE 0, x)ta-1(1-t)b-1dt/B(a,b) where B is the beta function. It is also the cumulative distribution function of the beta distribution.

betaIncomplete(a, b, x) evaluates Ix(a,b).

pure nothrow @safe @nogc
real
betaIncomplete
(
real a
,
real b
,
real x
)

Parameters

a real

the first argument of B, must be positive

b real

the second argument of B, must be positive

x real

the fraction of integration completion from below, 0 $(LE) x $(LE) 1

Return Value

Type: real

It returns Ix(a,b), an element of [0,1].

Note: The integral is evaluated by a continued fraction expansion or, when b * x is small, by a power series.

See Also

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