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).

Returns:

n : ndarray

The number of events n such that bdtr(k, n, p) = y.

See also

bdtr

Notes

Formula 26.5.24 of [R320] is used to reduce the binomial distribution to the cumulative incomplete beta distribution.

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

Wrapper for the CDFLIB [R321] Fortran routine cdfbin.

References

[R320]

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

[R321]

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