scipy.special.nbdtr¶

scipy.special.
nbdtr
(k, n, p) = <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).
 Returns
 Fndarray
The probability of k or fewer failures before n successes in a sequence of events with individual success probability p.
See also
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/