VGAM (version 0.9-3)

exppois: The Exponential Poisson Distribution

Description

Density, distribution function, quantile function and random generation for the exponential poisson distribution.

Usage

dexppois(x, lambda, betave = 1, log = FALSE)
pexppois(q, lambda, betave = 1)
qexppois(p, lambda, betave = 1)  
rexppois(n, lambda, betave = 1)

Arguments

x, q

vector of quantiles.

p

vector of probabilities.

n

number of observations. If length(n) > 1 then the length is taken to be the number required.

lambda, betave

both positive parameters.

log

Logical. If log = TRUE then the logarithm of the density is returned.

Value

• dexppois gives the density, pexppois gives the distribution function, qexppois gives the quantile function, and rexppois generates random deviates.

Details

See exppoisson, the VGAM family function for estimating the parameters, for the formula of the probability density function and other details.

See Also

exppoisson.

Examples

lambda <- 2; betave <- 2; nn <- 201
x <- seq(-0.05, 1.05, len = nn)
plot(x, dexppois(x, lambda, betave), type = "l", las = 1, ylim = c(0, 5),
     ylab = paste("[dp]exppoisson(lambda = ", lambda, ", betave = ", betave, ")"),
     col = "blue", cex.main = 0.8,
     main = "Blue is density, orange is cumulative distribution function",
     sub = "Purple lines are the 10,20,...,90 percentiles")
lines(x, pexppois(x, lambda, betave), col = "orange")
probs <- seq(0.1, 0.9, by = 0.1)
Q <- qexppois(probs, lambda, betave)
lines(Q, dexppois(Q, lambda, betave), col = "purple", lty = 3, type = "h")
lines(Q, pexppois(Q, lambda, betave), col = "purple", lty = 3, type = "h")
abline(h = probs, col = "purple", lty = 3)
max(abs(pexppois(Q, lambda, betave) - probs))  # Should be 0