scipy.special.nbdtrin — SciPy v1.15.2 Manual (original) (raw)
scipy.special.nbdtrin(k, y, p, out=None) = <ufunc 'nbdtrin'>#
Inverse of nbdtr vs n.
Returns the inverse with respect to the parameter n ofy = nbdtr(k, n, p), the negative binomial cumulative distribution function.
Parameters:
karray_like
The maximum number of allowed failures (nonnegative int).
yarray_like
The probability of k or fewer failures before n successes (float).
parray_like
Probability of success in a single event (float).
outndarray, optional
Optional output array for the function results
Returns:
nscalar or ndarray
The number of successes n such that nbdtr(k, n, p) = y.
See also
Cumulative distribution function of the negative binomial.
Inverse with respect to p of nbdtr(k, n, p).
Inverse with respect to k of nbdtr(k, n, p).
Notes
Wrapper for the CDFLIB [1] Fortran routine cdfnbn.
Formula 26.5.26 of [2],
\[\sum_{j=k + 1}^\infty {{n + j - 1} \choose{j}} p^n (1 - p)^j = I_{1 - p}(k + 1, n),\]
is used to reduce calculation of the cumulative distribution function to that of a regularized incomplete beta \(I\).
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.
References
[1]
Barry Brown, James Lovato, and Kathy Russell, CDFLIB: Library of Fortran Routines for Cumulative Distribution Functions, Inverses, and Other Parameters.
[2]
Milton Abramowitz and Irene A. Stegun, eds. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover, 1972.
Examples
Compute the negative binomial cumulative distribution function for an exemplary parameter set.
from scipy.special import nbdtr, nbdtrin k, n, p = 5, 2, 0.5 cdf_value = nbdtr(k, n, p) cdf_value 0.9375
Verify that nbdtrin recovers the original value for n up to floating point accuracy.
nbdtrin(k, cdf_value, p) 1.999999999998137