expgeometricUC: The Exponential Geometric Distribution

In VGAM: Vector Generalized Linear and Additive Models

The Exponential Geometric Distribution

Description

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.

Details

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

Value

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

Note

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

Author(s)

J. G. Lauder and T. W. Yee

See Also

expgeometric, exponential, geometric.

Examples

## Not run: 
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

## End(Not run)

VGAM documentation built on Sept. 18, 2024, 9:09 a.m.