nbconv - Evaluate Arbitrary Negative Binomial Convolutions

Five distinct methods are implemented for evaluating the sums of arbitrary negative binomial distributions. These methods are: Furman's exact series representation (Furman (2007) <doi:10.1016/j.spl.2006.06.007>), an FFT-based approach, a "hybrid" approach that uses FFT for non-extreme probabilities and falls back to the series representation for extremely low probabilities, saddlepoint approximation, and a method-of-moments approximation. Functions are provided to calculate probability masses, cumulative probabilities, and quantiles of the convolutions in question using said evaluation methods. Functions for generating random deviates from negative binomial convolutions and for directly calculating the mean, variance, skewness, and excess kurtosis from cumulants are also provided.