SciPy

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 [R316] routine bdtr.

References

[R316](1, 2) Cephes Mathematical Functions Library, http://www.netlib.org/cephes/index.html