VGAM (version 0.9-6)

Gompertz: The Gompertz Distribution

Description

Density, cumulative distribution function, quantile function and random generation for the Gompertz distribution.

Usage

dgompertz(x, scale = 1, shape, log = FALSE)
pgompertz(q, scale = 1, shape)
qgompertz(p, scale = 1, shape)
rgompertz(n, scale = 1, shape)

Arguments

x, q

vector of quantiles.

p

vector of probabilities.

n

number of observations. Same as in runif.

log

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

scale, shape

positive scale and shape parameters.

Value

• dgompertz gives the density, pgompertz gives the cumulative distribution function, qgompertz gives the quantile function, and rgompertz generates random deviates.

Details

See gompertz for details.

See Also

gompertz, dgumbel, dmakeham.

Examples

probs <- seq(0.01, 0.99, by = 0.01)
Shape <- exp(1); Scale <- exp(1)
max(abs(pgompertz(qgompertz(p = probs, Scale, shape = Shape),
                  Scale, shape = Shape) - probs))  # Should be 0

x <- seq(-0.1, 1.0, by = 0.001)
plot(x, dgompertz(x, Scale,shape = Shape), type = "l", col = "blue", las = 1,
     main = "Blue is density, orange is cumulative distribution function",
     sub = "Purple lines are the 10,20,...,90 percentiles",
     ylab = "")
abline(h = 0, col = "blue", lty = 2)
lines(x, pgompertz(x, Scale, shape = Shape), col = "orange")
probs <- seq(0.1, 0.9, by = 0.1)
Q <- qgompertz(probs, Scale, shape = Shape)
lines(Q, dgompertz(Q, Scale, shape = Shape), col = "purple",
      lty = 3, type = "h")
pgompertz(Q, Scale, shape = Shape) - probs  # Should be all zero
abline(h = probs, col = "purple", lty = 3)