polyaAeppli-package: The Polya-Aeppli distribution

Description Details Author(s) References Examples

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



polyaAeppli documentation built on May 2, 2019, 2:48 p.m.