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Version:

1.6

Date:

2024-08-23

Title:

The Poisson Binomial Distribution

Author:

Yili Hong [aut, cre], R Core Team [aut, cph]

Maintainer:

Yili Hong <yilihong@vt.edu>

Description:

Implementation of both the exact and approximation methods for computing the cdf of the Poisson binomial distribution as described in Hong (2013) <doi:10.1016/j.csda.2012.10.006>. It also provides the pmf, quantile function, and random number generation for the Poisson binomial distribution. The C code for fast Fourier transformation (FFT) is written by R Core Team (2019)https://www.R-project.org/, which implements the FFT algorithm in Singleton (1969) <doi:10.1109/TAU.1969.1162042>.

License:

GPL-2

NeedsCompilation:

yes

Packaged:

2024-08-23 14:18:07 UTC; yilih

Repository:

CRAN

Date/Publication:

2024-08-23 15:10:01 UTC

The Poisson Binomial Distribution

Description

Implementation of both the exact and approximation methods for computing the cdf of the Poisson binomial distribution as described in Hong (2013) <doi: 10.1016/j.csda.2012.10.006>. It also provides the pmf, quantile function, and random number generation for the Poisson binomial distribution. The C code for fast Fourier transformation (FFT) is written by R Core Team (2019)<https://www.R-project.org/>, which implements the FFT algorithm in Singleton (1969) <doi: 10.1109/TAU.1969.1162042>.

Details

Package:	poibin
Version:	1.6
Date:	2024-08-23
Title:	The Poisson Binomial Distribution
Authors@R:	c(person("Yili", "Hong", role = c("aut", "cre"),email = "yilihong@vt.edu"),person("", "R Core Team", role = c("aut", "cph")))
Author:	Yili Hong [aut, cre], R Core Team [aut, cph]
Maintainer:	Yili Hong <yilihong@vt.edu>
Description:	Implementation of both the exact and approximation methods for computing the cdf of the Poisson binomial distribution as described in Hong (2013) <doi: 10.1016/j.csda.2012.10.006>. It also provides the pmf, quantile function, and random number generation for the Poisson binomial distribution. The C code for fast Fourier transformation (FFT) is written by R Core Team (2019)<https://www.R-project.org/>, which implements the FFT algorithm in Singleton (1969) <doi: 10.1109/TAU.1969.1162042>.
License:	GPL-2
Archs:	x64

Index of help topics:

poibin-package          The Poisson Binomial Distribution
ppoibin                 The Poisson Binomial Distribution.

Author(s)

Yili Hong [aut, cre], R Core Team [aut, cph]

Maintainer: Yili Hong <yilihong@vt.edu>

References

Hong, Y. (2013). On computing the distribution function for the Poisson binomial distribution. Computational Statistics & Data Analysis, Vol. 59, pp. 41-51.

R Core Team (2019). “R: A Language and Environment for Statistical Computing,” R Foundation for Statistical Computing, Vienna, Austria, url: https://www.R-project.org/.

Singleton, R. C. (1969). An algorithm for computing the mixed radix fast Fourier transform. IEEE Transactions on Audio and Electroacoustics, Vol. 17, pp. 93-103.

Examples

   kk=0:10
   pp=c(.1,.2,.3,.4,.5)
   ppoibin(kk=kk, pp=pp, method = "DFT-CF",wts=rep(2,5))
   ppoibin(kk=kk, pp=pp, method = "RF",wts=rep(2,5))
   ppoibin(kk=kk, pp=pp, method = "RNA",wts=rep(2,5))
   ppoibin(kk=kk, pp=pp, method = "NA",wts=rep(2,5))
   ppoibin(kk=kk, pp=pp, method = "PA",wts=rep(2,5))
   dpoibin(kk=kk, pp=pp,wts=rep(2,5))
   qpoibin(qq=0:10/10,pp=pp,wts=rep(2,5))
   rpoibin(m=2,pp=pp,wts=rep(2,5))

The Poisson Binomial Distribution.

Description

The cdf, pmf, quantile function, and random number generation for the Poisson binomial distribution.

Usage

ppoibin(kk, pp, method = "DFT-CF",wts=NULL)
dpoibin(kk, pp,wts=NULL)
qpoibin(qq, pp,wts=NULL)
rpoibin(m, pp,wts=NULL)

Arguments

kk

The values where the cdf or pmf to be evaluated.

pp

The vector for p_j's which are the sucess probabilities for indicators.

method

"DFT-CF" for the DFT-CF method, "RF" for the recursive formula, "RNA" for the refined normal approximation, "NA" for the normal approximation, and "PA" for the Poisson approximation.

wts

The weights for p_j's.

qq

The values where the quantile function to be evaluated.

m

The number of random numbers to be generated.

Details

See the reference for computational details.

Value

Returns the entire cdf, pmf, quantiles, and random numbers.

Author(s)

Yili Hong [aut, cre], R Core Team [aut, cph]

References

Hong, Y. (2013). On computing the distribution function for the Poisson binomial distribution. Computational Statistics & Data Analysis, Vol. 59, pp. 41-51.

Examples

   kk=0:10
   pp=c(.1,.2,.3,.4,.5)
   ppoibin(kk=kk, pp=pp, method = "DFT-CF",wts=rep(2,5))
   ppoibin(kk=kk, pp=pp, method = "RF",wts=rep(2,5))
   ppoibin(kk=kk, pp=pp, method = "RNA",wts=rep(2,5))
   ppoibin(kk=kk, pp=pp, method = "NA",wts=rep(2,5))
   ppoibin(kk=kk, pp=pp, method = "PA",wts=rep(2,5))
   dpoibin(kk=kk, pp=pp,wts=rep(2,5))
   qpoibin(qq=0:10/10,pp=pp,wts=rep(2,5))
   rpoibin(m=2,pp=pp,wts=rep(2,5))