VGAM (version 1.1-8)

Gompertz: 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, lower.tail = TRUE, log.p = FALSE)
qgompertz(p, scale = 1, shape, lower.tail = TRUE, log.p = FALSE)
rgompertz(n, scale = 1, shape)

Value

dgompertz gives the density,

pgompertz gives the cumulative distribution function,

qgompertz gives the quantile function, and

rgompertz generates random deviates.

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.

lower.tail, log.p

Same meaning as in pnorm or qnorm.

scale, shape

positive scale and shape parameters.

Author

T. W. Yee and Kai Huang

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

if (FALSE)  x <- seq(-0.1, 1.0, by = 0.001)
plot(x, dgompertz(x, Scale,shape = Shape), type = "l", las = 1,
     main = "Blue is density, orange is the CDF", col = "blue",
     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)