scipy.special.nbdtrc¶
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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
- 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 + 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/