scipy.special.nbdtr

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

Negative binomial cumulative distribution function.

Returns the sum of the terms 0 through k of the negative binomial distribution probability mass function,

\[F = \sum_{j=0}^k {{n + j - 1}\choose{j}} p^n (1 - p)^j.\]

In a sequence of Bernoulli trials with individual success probabilities p, this is the probability that k or fewer failures precede the nth success.

Parameters

karray_like

The maximum number of allowed failures (nonnegative int).

narray_like

The target number of successes (positive int).

parray_like

Probability of success in a single event (float).

outndarray, optional

Optional output array for the function results

Returns

Fscalar or ndarray

The probability of k or fewer failures before n successes in a sequence of events with individual success probability p.

See also

nbdtrc

Notes

If floating point values are passed for k or n, they will be truncated to integers.

The terms are not summed directly; instead the regularized incomplete beta function is employed, according to the formula,

\[\mathrm{nbdtr}(k, n, p) = I_{p}(n, k + 1).\]

Wrapper for the Cephes [1] routine nbdtr.

References

1

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