# incbet¶

sherpa.utils.incbet(a, b, x)[source] [edit on github]

Calculate the incomplete Beta function.

The function is defined as:

```sqrt(a+b)/(sqrt(a) sqrt(b)) Int_0^x t^(a-1) (1-t)^(b-1) dt
```

and the integral from x to 1 can be obtained using the relation:

```1 - incbet(a, b, x) = incbet(b, a, 1-x)
```
Parameters
• a (scalar or array) – a > 0

• b (scalar or array) – b > 0

• x (scalar or array) – 0 <= x <= 1

Returns

val – The incomplete beta function calculated from the inputs.

Return type

scalar or array

Notes

In this implementation, which is provided by the Cephes Math Library 1, the integral is evaluated by a continued fraction expansion or, when b*x is small, by a power series.

Using IEEE arithmetic, the relative errors are (tested uniformly distributed random points (a,b,x) with a and b in ‘domain’ and x between 0 and 1):

domain

# trials

peak

rms

0,5

10000

6.9e-15

4.5e-16

0,85

250000

2.2e-13

1.7e-14

0,1000

30000

5.3e-12

6.3e-13

0,1000

250000

9.3e-11

7.1e-12

0,100000

10000

8.7e-10

4.8e-11

Outputs smaller than the IEEE gradual underflow threshold were excluded from these statistics.

References

1

Cephes Math Library Release 2.0: April, 1987. Copyright 1985, 1987 by Stephen L. Moshier. Direct inquiries to 30 Frost Street, Cambridge, MA 02140.

Examples

```>>> incbet(0.3, 0.6, 0.5)
0.68786273145845922
```
```>>> incbet([0.3,0.3], [0.6,0.7], [0.5,0.4])
array([ 0.68786273,  0.67356524])
```