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.
Relative error
| IEEE |
0,5 |
10000 |
6.9e-15 |
4.5e-16 |
| IEEE |
0,85 |
250000 |
2.2e-13 |
1.7e-14 |
| IEEE |
0,1000 |
30000 |
5.3e-12 |
6.3e-13 |
| IEEE |
0,10000 |
250000 |
9.3e-11 |
7.1e-12 |
| IEEE |
0,100000 |
10000 |
8.7e-10 |
4.8e-11 |
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.
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