# polyaAeppli-package: The Polya-Aeppli distribution In polyaAeppli: Implementation of the Polya-Aeppli distribution

## Description

Functions for evaluating the mass density, cumulative distribution function, quantile function and random variate generation for the Polya-Aeppli distribution, also known as the geometric compound Poisson distribution.

## Details

 Package: polyaAeppli Type: Package Version: 2.0 Depends: R (>= 3.0.0) Date: 2014-03-14 License: GPL(>=2)

Consistent with the conventions used in R package stats, this implementation of the Polya-Aeppli distribution comprises the four functions

`dPolyaAeppli(x, lambda, prob, log = FALSE)`
`pPolyaAeppli(q, lambda, prob, lower.tail = TRUE, log.p = FALSE)`
`qPolyaAeppli(p, lambda, prob, lower.tail = TRUE, log.p = FALSE)`
`rPolyaAeppli(n, lambda, prob)`

## Author(s)

Conrad Burden

Maintainer: conrad.burden@anu.edu.au

## References

Johnson NL, Kotz S, Kemp AW (1992). Univariate Discrete Distributions. 2nd edition. Wiley, New York.

Nuel G (2008). Cumulative distribution function of a geometeric Poisson distribution. Journal of Statistical Computation and Simulation, 78(3), 385-394.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23``` ```lambda <- 8 prob <- 0.2 ## Plot histogram of random sample PAsample <- rPolyaAeppli(10000, lambda, prob) maxPA <- max(PAsample) hist(PAsample, breaks=(0:(maxPA + 1)) - 0.5, freq=FALSE, xlab = "x", ylab = expression(P[X](x)), main="", border="blue") ## Add plot of density function x <- 0:maxPA points(x, dPolyaAeppli(x, lambda, prob), type="h", lwd=2) lambda <- 4000 prob <- 0.005 qq <- 0:10000 ## Plot log of the extreme lower tail p-value log.pp <- pPolyaAeppli(qq, lambda, prob, log.p=TRUE) plot(qq, log.pp, type = "l", ylim=c(-lambda,0), xlab = "x", ylab = expression("log Pr(X " <= "x)")) ## Plot log of the extreme upper tail p-value log.1minuspp <- pPolyaAeppli(qq, lambda, prob, log.p=TRUE, lower.tail=FALSE) points(qq, log.1minuspp, type = "l", col = "red") legend("topright", c("lower tail", "upper tail"), col=c("black", "red"), lty=1, bg="white") ```

### Example output  ```
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polyaAeppli documentation built on May 2, 2019, 2:48 p.m.