pgpb: Generalized Poisson Binomial Distribution In GPB: Generalized Poisson Binomial Distribution

Description

The cdf, pmf, quantile function, and random number generator function for Generalized Poisson Binomial distribution.

Usage

 1 2 3 4 5 pgpb(kk, pp, aval, bval, wts = NULL) dgpb(kk, pp, aval, bval, wts = NULL) qgpb(qq, pp, aval, bval, wts = NULL) rgpb(m, pp, aval, bval, wts = NULL) gpb.args.check(pp, aval, bval, wts)

Arguments

 kk The values where the cdf or pmf to be evaluated. pp The vector for p_k's which are the sucess probabilities for indicators. aval The smaller possible values of each indicator, default to be 0. Integer values needed. bval The larger possible values of each indicator, default to be 1. Integer values needed. wts The weights for p_k's. Positive integer values needed. qq The values where the quantile function to be evaluated. m The number of random numbers to be generated.

Value

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

Author(s)

Yili Hong [aut, cre], Man Zhang [aut, ctb], R Core Team [aut, cph]

References

Man. Zhang, Y. Hong, and N. Balakrishnan (2018). “The generalized Poisson-binomial distribution and the computation of its distribution function,” Journal of Statistical Computation and Simulation, Vol. 88, pp. 1515-1527.

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

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 pgpb(kk=0:11, pp=c(.1, .2, .3), aval=c(1,0,0), bval=c(2,3,1), wts=c(1,2,2)) dgpb(kk=0:11, pp=c(.1, .2, .3), aval=c(1,0,0), bval=c(2,3,1), wts=c(1,2,2)) qgpb(qq=c(.1,.3), pp=c(.1, .2, .3), aval=c(1,0,0), bval=c(2,3,1), wts=c(1,2,2)) rgpb(m=3, pp=c(.1, .2, .3), aval=c(1,0,0), bval=c(2,3,1), wts=c(1,2,2)) ## when a, b share large common dividers, the results of following cases is the same pgpb(kk=c(60,70,80,90), pp=c(.1, .2, .3), aval=c(10,20,30), bval=c(20,30,40), wts=c(1,1,1)) pgpb(kk=6:9, pp=c(.1, .2, .3), aval=c(1,2,3), bval=c(2,3,4), wts=c(1,1,1)) ## when a, b are non-integer values, the values of kk, aval, bval can multiply powers of 10 aval=c(0.1,0.2,0.3)*10 bval=c(0.2,0.3,0.4)*10 kk=(0.6*10):(1.0*10) pgpb(kk=kk, pp=c(.1, .2, .3), aval=aval, bval=bval, wts=c(1,1,1))

GPB documentation built on Jan. 8, 2020, 1:08 a.m.