# 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). 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 [R315] routine bdtr.

References

 [R315] (1, 2) Cephes Mathematical Functions Library, http://www.netlib.org/cephes/index.html

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