# scipy.special.bdtrin¶

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

Inverse function to bdtr with respect to n.

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

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

Notes

Formula 26.5.24 of [1] is used to reduce the binomial distribution to the cumulative incomplete beta distribution.

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.

Wrapper for the CDFLIB [2] Fortran routine cdfbin.

References

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

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