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# scipy.special.bdtrik

`scipy.special.``bdtrik`(y, n, p) = <ufunc 'bdtrik'>

  Inverse function to `bdtr` with respect to k.

  Finds the number of successes k such that the sum of the terms 0 through k of the Binomial probability density for n events with probability p is equal to the given cumulative probability y.

  Parameters: | y : array_like Cumulative probability (probability of k or fewer successes in n events). n : array_like Number of events (float). p : array_like Success probability (float).
  Returns: | k : ndarray The number of successes k such that bdtr(k, n, p) = y.

  See also

  `bdtr`

  Notes

  Formula 26.5.24 of [R374] is used to reduce the binomial distribution to the cumulative incomplete beta distribution.

  Computation of k involves a seach for a value that produces the desired value of y. The search relies on the monotinicity of y with k.

  Wrapper for the CDFLIB [R375] Fortran routine cdfbin.

  References

  [R374] | (1, 2) Milton Abramowitz and Irene A. Stegun, eds. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover, 1972.

  [R375] | (1, 2) Barry Brown, James Lovato, and Kathy Russell, CDFLIB: Library of Fortran Routines for Cumulative Distribution Functions, Inverses, and Other Parameters.