# scipy.special.nbdtrc

scipy.special.nbdtrc(k, n, p) = <ufunc 'nbdtrc'>

  Negative binomial survival function.

  Returns the sum of the terms k + 1 to infinity of the negative binomial distribution probability mass function,

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

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

  Parameters
    k array_like

      The maximum number of allowed failures (nonnegative int).

    n array_like

      The target number of successes (positive int).

    p array_like

      Probability of success in a single event (float).

  Returns
    F ndarray

      The probability of k + 1 or more failures before n successes in a sequence of events with individual success probability p.

  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,

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

  Wrapper for the Cephes [1] routine `nbdtrc`.

  References

  1

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

scipy.special.nbdtr scipy.special.nbdtri