scipy.special.nbdtri#
- scipy.special.nbdtri(k, n, y, out=None) = <ufunc 'nbdtri'>#
- Returns the inverse with respect to the parameter p of - y = nbdtr(k, n, p), the negative binomial cumulative distribution function.- Parameters:
- karray_like
- The maximum number of allowed failures (nonnegative int). 
- narray_like
- The target number of successes (positive int). 
- yarray_like
- The probability of k or fewer failures before n successes (float). 
- outndarray, optional
- Optional output array for the function results 
 
- Returns:
- pscalar or ndarray
- Probability of success in a single event (float) such that nbdtr(k, n, p) = y. 
 
 - See also - nbdtr
- Cumulative distribution function of the negative binomial. 
- nbdtrc
- Negative binomial survival function. 
- scipy.stats.nbinom
- negative binomial distribution. 
- nbdtrik
- Inverse with respect to k of nbdtr(k, n, p). 
- nbdtrin
- Inverse with respect to n of nbdtr(k, n, p). 
- scipy.stats.nbinom
- Negative binomial distribution 
 - Notes - Wrapper for the Cephes [1] routine - nbdtri.- The negative binomial distribution is also available as - scipy.stats.nbinom. Using- nbdtridirectly can improve performance compared to the- ppfmethod of- scipy.stats.nbinom.- References [1]- Cephes Mathematical Functions Library, http://www.netlib.org/cephes/ - Examples - nbdtriis the inverse of- nbdtrwith respect to p. Up to floating point errors the following holds:- nbdtri(k, n, nbdtr(k, n, p))=p.- >>> import numpy as np >>> from scipy.special import nbdtri, nbdtr >>> k, n, y = 5, 10, 0.2 >>> cdf_val = nbdtr(k, n, y) >>> nbdtri(k, n, cdf_val) 0.20000000000000004 - Compute the function for - k=10and- n=5at several points by providing a NumPy array or list for y.- >>> y = np.array([0.1, 0.4, 0.8]) >>> nbdtri(3, 5, y) array([0.34462319, 0.51653095, 0.69677416]) - Plot the function for three different parameter sets. - >>> import matplotlib.pyplot as plt >>> n_parameters = [5, 20, 30, 30] >>> k_parameters = [20, 20, 60, 80] >>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot'] >>> parameters_list = list(zip(n_parameters, k_parameters, linestyles)) >>> cdf_vals = np.linspace(0, 1, 1000) >>> fig, ax = plt.subplots(figsize=(8, 8)) >>> for parameter_set in parameters_list: ... n, k, style = parameter_set ... nbdtri_vals = nbdtri(k, n, cdf_vals) ... ax.plot(cdf_vals, nbdtri_vals, label=rf"$k={k},\ n={n}$", ... ls=style) >>> ax.legend() >>> ax.set_ylabel("$p$") >>> ax.set_xlabel("$CDF$") >>> title = "nbdtri: inverse of negative binomial CDF with respect to $p$" >>> ax.set_title(title) >>> plt.show()   - nbdtrican evaluate different parameter sets by providing arrays with shapes compatible for broadcasting for k, n and p. Here we compute the function for three different k at four locations p, resulting in a 3x4 array.- >>> k = np.array([[5], [10], [15]]) >>> y = np.array([0.3, 0.5, 0.7, 0.9]) >>> k.shape, y.shape ((3, 1), (4,)) - >>> nbdtri(k, 5, y) array([[0.37258157, 0.45169416, 0.53249956, 0.64578407], [0.24588501, 0.30451981, 0.36778453, 0.46397088], [0.18362101, 0.22966758, 0.28054743, 0.36066188]])