scipy.special.bdtr

scipy.special.bdtr(k, n, p, out=None) = <ufunc 'bdtr'>

Binomial distribution cumulative distribution function.

Sum of the terms 0 through floor(k) of the Binomial probability density.

\[\mathrm{bdtr}(k, n, p) = \sum_{j=0}^{\lfloor k \rfloor} {{n}\choose{j}} p^j (1-p)^{n-j}\]

Parameters:

karray_like

Number of successes (double), rounded down to the nearest integer.

narray_like

Number of events (int).

parray_like

Probability of success in a single event (float).

outndarray, optional

Optional output array for the function values

Returns:

yscalar or ndarray

Probability of floor(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,

\[\mathrm{bdtr}(k, n, p) = I_{1 - p}(n - \lfloor k \rfloor, \lfloor k \rfloor + 1).\]

Wrapper for the Cephes [1] routine bdtr.

References

[1]

Cephes Mathematical Functions Library, http://www.netlib.org/cephes/