# Implementation of the Polya-Aeppli Distribution 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. More information on the implementation of polyaAeppli can be found at Conrad J. Burden (2014) . package ## Details ||| |:--|:--| |Package:|polyaAeppli| |Type:|Package| |Version:|2.0.2| |Depends:|R (>= 3.0.0)| |Date:|2020-04-21| |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 ```r 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") ```

polyaAeppli-package