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/