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/