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Function `std.mathspecial.betaIncomplete`

Incomplete beta integral


						
				real betaIncomplete(
				
  real a,
				
  real b,
				
  real x
				

				) pure nothrow @nogc @safe;

Returns regularized incomplete beta integral of the arguments, evaluated from zero to x. The regularized incomplete beta function is defined as

betaIncomplete(a, b, x) = Γ(a + b) / ( Γ(a) Γ(b) ) * ∫₀^x t^a-1(1-t)^b-1 dt

and is the same as the cumulative distribution function of the Beta distribution.

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

betaIncompleteCompl(a, b, x ) = betaIncomplete( b, a, 1-x )

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

Authors

Stephen L. Moshier (original C code). Conversion to D by Don Clugston

License

Boost License 1.0.

API Documentation

Function std.mathspecial.betaIncomplete

Authors

License

Function `std.mathspecial.betaIncomplete`