PoissonBinomial-package {PoissonBinomial}

Efficient Exact and Approximate Implementations for Computing Ordinary and Generalized Poisson Binomial Distributions

Description

This package implements various algorithms for computing the probability mass function, the cumulative distribution function, quantiles and random numbers of both ordinary and generalized Poisson binomial distributions.

References

Hong, Y. (2013). On computing the distribution function for the Poisson binomial distribution. Computational Statistics & Data Analysis, 59, pp. 41-51. doi:10.1016/j.csda.2012.10.006

Biscarri, W., Zhao, S. D. and Brunner, R. J. (2018) A simple and fast method for computing the Poisson binomial distribution. Computational Statistics and Data Analysis, 31, pp. 216–222. doi:10.1016/j.csda.2018.01.007

Zhang, M., Hong, Y. and Balakrishnan, N. (2018). The generalized Poisson-binomial distribution and the computation of its distribution function. Journal of Statistical Computational and Simulation, 88(8), pp. 1515-1527. doi:10.1080/00949655.2018.1440294

Examples

# Functions for ordinary Poisson binomial distributions
set.seed(1)
pp <- c(1, 0, runif(10), 1, 0, 1)
qq <- seq(0, 1, 0.01)

dpbinom(NULL, pp)
ppbinom(7:10, pp, method = "DivideFFT")
qpbinom(qq, pp, method = "Convolve")
rpbinom(10, pp, method = "RefinedNormal")

# Functions for generalized Poisson binomial distributions
va <- rep(5, length(pp))
vb <- 1:length(pp)

dgpbinom(NULL, pp, va, vb, method = "Convolve")
pgpbinom(80:100, pp, va, vb, method = "Convolve")
qgpbinom(qq, pp, va, vb, method = "Convolve")
rgpbinom(100, pp, va, vb, method = "Convolve")