Gompertz {VGAM}

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)

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.

Details

See gompertz for details.

Value

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

Author(s)

T. W. Yee and Kai Huang

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

## Not run:  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) 
## End(Not run)