.. py:function:: bdtrc(k, n, p)
Returns the sum of the terms k + 1 through n of the Binomial
probability density:
:param int k: number of successes within [0, n]
:param int n: number of trials
:param float p: probability of success within [0, 1]
See also :py:func:`bdtr` and :py:func:`bdtri`.
\sum_{j=k+1}^n {n \choose j} p^j (1-p)^{n-j}
The terms are not summed directly; instead the incomplete beta integral is employed, according to the formula:
y = bdtrc( k, n, p ) = incbet( k+1, n-k, p )
The arguments must be positive, with p ranging from 0 to 1.
Tested at random points (a, b, p).
| a, b | relative error | |||
|---|---|---|---|---|
| arithmetic | domain | # trials | peak | rms |
| For p between 0.001 and 1 | ||||
| IEEE | 0, 100 | 100000 | 6.7e-15 | 8.2e-16 |
| For p between 0 and .001 | ||||
| IEEE | 0, 100 | 100000 | 1.5e-13 | 2.7e-15 |
| message | condition | value returned |
|---|---|---|
| bdtrc domain | x < 0, x > 1, n < k | 0.0 |