# scipy.special.nbdtrin¶

scipy.special.nbdtrin(k, y, p) = <ufunc 'nbdtrin'>

Inverse of nbdtr vs n.

Returns the inverse with respect to the parameter n of y = nbdtr(k, n, p), the negative binomial cumulative distribution function.

Parameters: k : array_like The maximum number of allowed failures (nonnegative int). y : array_like The probability of k or fewer failures before n successes (float). p : array_like Probability of success in a single event (float). n : ndarray The number of successes n such that nbdtr(k, n, p) = y.

nbdtr
Cumulative distribution function of the negative binomial.
nbdtri
Inverse with respect to p of nbdtr(k, n, p).
nbdtrik
Inverse with respect to k of nbdtr(k, n, p).

Notes

Wrapper for the CDFLIB  Fortran routine cdfnbn.

Formula 26.5.26 of ,

$\sum_{j=k + 1}^\infty {{n + j - 1}\choose{j}} p^n (1 - p)^j = I_{1 - p}(k + 1, n),$

is used to reduce calculation of the cumulative distribution function to that of a regularized incomplete beta $$I$$.

Computation of n involves a search for a value that produces the desired value of y. The search relies on the monotonicity of y with n.

References

  (1, 2) Barry Brown, James Lovato, and Kathy Russell, CDFLIB: Library of Fortran Routines for Cumulative Distribution Functions, Inverses, and Other Parameters.
  (1, 2) Milton Abramowitz and Irene A. Stegun, eds. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover, 1972.

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