scipy.special.bdtrin#

scipy.special.bdtrin(k,y,p,out=None)=<ufunc'bdtrin'>#

Inverse function tobdtr with respect ton.

Finds the number of eventsn such that the sum of the terms 0 throughk of the Binomial probability density for events with probabilityp isequal to the given cumulative probabilityy.

Parameters:

karray_like

Number of successes (float).

yarray_like

Cumulative probability (probability ofk or fewer successes innevents).

parray_like

Success probability (float).

outndarray, optional

Optional output array for the function values

Returns:

nscalar or ndarray

The number of eventsn such thatbdtr(k, n, p) = y.

See also

bdtr

Notes

Formula 26.5.24 of[1] (or equivalently[2]) is used to reduce the binomialdistribution to the cumulative incomplete beta distribution.

Computation ofn involves a search for a value that produces the desiredvalue ofy. The search relies on the monotonicity ofy withn.

Wrapper for the CDFLIB[3] Fortran routinecdfbin.

References

[1]

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

[2]

NIST Digital Library of Mathematical Functionshttps://dlmf.nist.gov/8.17.5#E5

[3]

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