# ppoibin: The Poisson Binomial Distribution. In poibin: The Poisson Binomial Distribution

## Description

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

## Usage

 ```1 2 3 4``` ```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

 ``` 1 2 3 4 5 6 7 8 9 10``` ``` 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)) ```

### Example output

```  0.02286144 0.13517280 0.37211652 0.65383500 0.86212984 0.96181016
 0.99294500 0.99918348 0.99994720 0.99999856 1.00000000
 0.02286144 0.13517280 0.37211652 0.65383500 0.86212984 0.96181016
 0.99294500 0.99918348 0.99994720 0.99999856 1.00000000
 0.02812958 0.13669805 0.37078646 0.65398594 0.86019757 0.95840421
 0.99114093 0.99873860 0.99988766 0.99999400 0.99999981
 0.03486268 0.13825024 0.35840026 0.64159974 0.86174976 0.96513732
 0.99444416 0.99945199 0.99996698 0.99999879 0.99999997
 0.04978707 0.19914827 0.42319008 0.64723189 0.81526324 0.91608206
 0.96649146 0.98809550 0.99619701 0.99889751 0.99970766
 0.02286144 0.11231136 0.23694372 0.28171848 0.20829484 0.09968032
 0.03113484 0.00623848 0.00076372 0.00005136 0.00000144
  0  1  2  2  3  3  3  4  4  5 10
 5 5
```

poibin documentation built on Jan. 9, 2020, 1:09 a.m.