scipy.special.bdtrik

scipy.special.bdtrik(y, n, p, out=None) = <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

yarray_like

Cumulative probability (probability of k or fewer successes in n events).

narray_like

Number of events (float).

parray_like

Success probability (float).

outndarray, optional

Optional output array for the function values

Returns

kscalar or ndarray

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

See also

bdtr

Notes

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

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

Wrapper for the CDFLIB [2] Fortran routine cdfbin.

References

1

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

2

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