scipy.special.nbdtrin

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

Inverse of nbdtr vs n.

Returns the inverse with respect to the parameter n of y = 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).

Returns

nndarray

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

See also

nbdtr

Cumulative distribution function of the negative binomial.

nbdtri

Inverse with respect to p of nbdtr(k, n, p).

nbdtrik

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(1,2)

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

2(1,2)

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