|AHELP for CIAO 4.5 Sherpa v1||
Calculate the incomplete Beta function
Calculate the CEPHES function, incbet, in the range [a > 0; b > 0; 0 <= x <= 1] . The function returns incomplete beta integral of the arguments (scalar or array based), evaluated from zero to x.
The function is defined as
sqrt(a+b)/[sqrt(a)sqrt(b)] Int_(0)^(x) t^(a-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
1 - incbet( a, b, x ) = incbet( b, a, 1-x ).
The integral is evaluated by a continued fraction expansion or, when b*x is small, by a power series.
Tested at uniformly distributed random points (a,b,x) with a and b in "domain" and x between 0 and 1.
Outputs smaller than the IEEE gradual underflow threshold were excluded from these statistics.
Cephes Math Library Release 2.0: April, 1987. Copyright 1985, 1987 by Stephen L. Moshier. Direct inquiries to 30 Frost Street, Cambridge, MA 02140.
Calculate incbet with a=0.3, b=0.6, x=0.5 .
Calculate incbet with a=[0.3], b=[0.6], x=[0.5] .
See the bugs pages on the Sherpa website for an up-to-date listing of known bugs.