scipy.special.nbdtrik#
- scipy.special.nbdtrik(y, n, p) = <ufunc 'nbdtrik'>#
Inverse of
nbdtrvs k.Returns the inverse with respect to the parameter k of y = nbdtr(k, n, p), the negative binomial cumulative distribution function.
- Parameters
- yarray_like
The probability of k or fewer failures before n successes (float).
- narray_like
The target number of successes (positive int).
- parray_like
Probability of success in a single event (float).
- Returns
- kndarray
The maximum number of allowed failures such that nbdtr(k, n, p) = y.
See also
Notes
Wrapper for the CDFLIB [1] Fortran routine cdfnbn.
Formula 26.5.26 of [2],
\[\sum_{j=k + 1}^\infty {{n + j - 1}\choose{j}} p^n (1 - p)^j = I_{1 - p}(k + 1, n),\]is used to reduce calculation of the cumulative distribution function to that of a regularized incomplete beta \(I\).
Computation of k involves a search for a value that produces the desired value of y. The search relies on the monotonicity of y with k.
References
- 1
Barry Brown, James Lovato, and Kathy Russell, CDFLIB: Library of Fortran Routines for Cumulative Distribution Functions, Inverses, and Other Parameters.
- 2
Milton Abramowitz and Irene A. Stegun, eds. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover, 1972.