# 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).

  Returns
    n ndarray

      The number of successes n such that nbdtr(k, n, p) = y.

  See also

  `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 [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 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

    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.

scipy.special.nbdtrik scipy.special.ncfdtr