The Makeham Distribution
Density, cumulative distribution function, quantile function and random generation for the Makeham distribution.
dmakeham(x, scale = 1, shape, epsilon = 0, log = FALSE) pmakeham(q, scale = 1, shape, epsilon = 0, lower.tail = TRUE, log.p = FALSE) qmakeham(p, scale = 1, shape, epsilon = 0, lower.tail = TRUE, log.p = FALSE) rmakeham(n, scale = 1, shape, epsilon = 0)
x, q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations.
Same as in |
log |
Logical.
If |
lower.tail, log.p |
|
scale, shape |
positive scale and shape parameters. |
epsilon |
another parameter. Must be non-negative. See below. |
dmakeham gives the density,
pmakeham gives the cumulative distribution function,
qmakeham gives the quantile function, and
rmakeham generates random deviates.
T. W. Yee and Kai Huang
Jodra, P. (2009). A closed-form expression for the quantile function of the Gompertz-Makeham distribution. Mathematics and Computers in Simulation, 79, 3069–3075.
probs <- seq(0.01, 0.99, by = 0.01)
Shape <- exp(-1); Scale <- exp(1); eps = Epsilon <- exp(-1)
max(abs(pmakeham(qmakeham(p = probs, sca = Scale, Shape, eps = Epsilon),
sca = Scale, Shape, eps = Epsilon) - probs)) # Should be 0
## Not run: x <- seq(-0.1, 2.0, by = 0.01);
plot(x, dmakeham(x, sca = Scale, Shape, eps = Epsilon), type = "l",
main = "Blue is density, orange is cumulative distribution function",
sub = "Purple lines are the 10,20,...,90 percentiles",
col = "blue", las = 1, ylab = "")
abline(h = 0, col = "blue", lty = 2)
lines(x, pmakeham(x, sca = Scale, Shape, eps = Epsilon), col = "orange")
probs <- seq(0.1, 0.9, by = 0.1)
Q <- qmakeham(probs, sca = Scale, Shape, eps = Epsilon)
lines(Q, dmakeham(Q, sca = Scale, Shape, eps = Epsilon),
col = "purple", lty = 3, type = "h")
pmakeham(Q, sca = Scale, Shape, eps = Epsilon) - probs # Should be all zero
abline(h = probs, col = "purple", lty = 3)
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.