The Exponential Geometric Distribution

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

Usage

dexpgeom(x, scale = 1, shape, log = FALSE)
pexpgeom(q, scale = 1, shape)
qexpgeom(p, scale = 1, shape) 
rexpgeom(n, scale = 1, shape)

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.

scale, shape

positive scale and shape parameters.

log

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

Value

dexpgeom gives the density, pexpgeom gives the distribution function, qexpgeom gives the quantile function, and rexpgeom generates random deviates.

Author

J. G. Lauder and T. W. Yee

Details

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

Note

We define scale as the reciprocal of the scale parameter used by Adamidis and Loukas (1998).

See also

expgeometric, exponential, geometric.

Examples

if (FALSE) { # \dontrun{
shape <- 0.5; scale <- 1; nn <- 501
x <- seq(-0.10, 3.0, len = nn)
plot(x, dexpgeom(x, scale, shape), type = "l", las = 1, ylim = c(0, 2),
     ylab = paste("[dp]expgeom(shape = ", shape, ", scale = ", scale, ")"),
     col = "blue", cex.main = 0.8,
     main = "Blue is density, red is cumulative distribution function",
     sub = "Purple lines are the 10,20,...,90 percentiles")
lines(x, pexpgeom(x, scale, shape), col = "red")
probs <- seq(0.1, 0.9, by = 0.1)
Q <- qexpgeom(probs, scale, shape)
lines(Q, dexpgeom(Q, scale, shape), col = "purple", lty = 3, type = "h")
lines(Q, pexpgeom(Q, scale, shape), col = "purple", lty = 3, type = "h")
abline(h = probs, col = "purple", lty = 3)
max(abs(pexpgeom(Q, scale, shape) - probs))  # Should be 0
} # }