SciPy

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 [R452] routine nbdtrc.

References

[R452](1, 2) Cephes Mathematical Functions Library, http://www.netlib.org/cephes/index.html

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