Gompertz Distribution

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

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.

Value

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

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
#> [1] 1.665335e-16

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 = "")
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'x' in selecting a method for function 'plot': object 'x' not found
abline(h = 0, col = "blue", lty = 2)
#> Error in int_abline(a = a, b = b, h = h, v = v, untf = untf, ...): plot.new has not been called yet
lines(x, pgompertz(x, Scale, shape = Shape), col = "orange")
#> Error: object 'x' not found
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")
#> Error in plot.xy(xy.coords(x, y), type = type, ...): plot.new has not been called yet
pgompertz(Q, Scale, shape = Shape) - probs  # Should be all zero
#> [1]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
#> [6]  0.000000e+00  1.110223e-16 -1.110223e-16  0.000000e+00
abline(h = probs, col = "purple", lty = 3)  # \dontrun{}
#> Error in int_abline(a = a, b = b, h = h, v = v, untf = untf, ...): plot.new has not been called yet