scipy.special.bdtr¶
-
scipy.special.
bdtr
(k, n, p) = <ufunc 'bdtr'>¶ Binomial distribution cumulative distribution function.
Sum of the terms 0 through k of the Binomial probability density.
\[\mathrm{bdtr}(k, n, p) = \sum_{j=0}^k {{n}\choose{j}} p^j (1-p)^{n-j}\]Parameters: - k : array_like
Number of successes (int).
- n : array_like
Number of events (int).
- p : array_like
Probability of success in a single event (float).
Returns: - y : ndarray
Probability of k or fewer successes in n independent events with success probabilities of p.
Notes
The terms are not summed directly; instead the regularized incomplete beta function is employed, according to the formula,
\[\mathrm{bdtr}(k, n, p) = I_{1 - p}(n - k, k + 1).\]Wrapper for the Cephes [1] routine
bdtr
.References
[1] (1, 2) Cephes Mathematical Functions Library, http://www.netlib.org/cephes/