scipy.special.nbdtrin#
- scipy.special.nbdtrin(k, y, p, out=None) = <ufunc 'nbdtrin'>#
- Inverse of - nbdtrvs 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). 
- 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 - 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 - nbdtrinrecovers the original value for n up to floating point accuracy.- >>> nbdtrin(k, cdf_value, p) 1.999999999998137