VGAM (version 0.9-6)

Dagum: The Dagum Distribution

Description

Density, distribution function, quantile function and random generation for the Dagum distribution with shape parameters a and p, and scale parameter scale.

Usage

ddagum(x, shape1.a, scale = 1, shape2.p, log = FALSE)
pdagum(q, shape1.a, scale = 1, shape2.p)
qdagum(p, shape1.a, scale = 1, shape2.p)
rdagum(n, shape1.a, scale = 1, shape2.p)

Arguments

x, q

vector of quantiles.

p

vector of probabilities.

n

number of observations. If length(n) > 1, the length is taken to be the number required.

shape1.a, shape2.p

shape parameters.

scale

scale parameter.

log

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

Value

• ddagum gives the density, pdagum gives the distribution function, qdagum gives the quantile function, and rdagum generates random deviates.

Details

See dagum, which is the VGAM family function for estimating the parameters by maximum likelihood estimation.

References

Kleiber, C. and Kotz, S. (2003) Statistical Size Distributions in Economics and Actuarial Sciences, Hoboken, NJ, USA: Wiley-Interscience.

See Also

dagum, genbetaII.

Examples

probs <- seq(0.1, 0.9, by = 0.1)
shape1.a <- 1; shape2.p <- 2
# Should be 0:
max(abs(pdagum(qdagum(p = probs, shape1.a = shape1.a, shape2.p =  shape2.p),
                                 shape1.a = shape1.a, shape2.p = shape2.p) - probs))

par(mfrow = c(1, 2))
x <- seq(-0.01, 5, len = 401)
plot(x, dexp(x), type = "l", col = "black", ylab = "", las = 1, ylim = c(0, 1),
     main = "Black is standard exponential, others are ddagum(x, ...)")
lines(x, ddagum(x, shape1.a = shape1.a, shape2.p = 1), col = "orange")
lines(x, ddagum(x, shape1.a = shape1.a, shape2.p = 2), col = "blue")
lines(x, ddagum(x, shape1.a = shape1.a, shape2.p = 5), col = "green")
legend("topright", col = c("orange","blue","green"), lty = rep(1, len = 3),
       legend = paste("shape1.a =", shape1.a, ", shape2.p =", c(1, 2, 5)))

plot(x, pexp(x), type = "l", col = "black", ylab = "", las = 1,
     main = "Black is standard exponential, others are pdagum(x, ...)")
lines(x, pdagum(x, shape1.a = shape1.a, shape2.p = 1), col = "orange")
lines(x, pdagum(x, shape1.a = shape1.a, shape2.p = 2), col = "blue")
lines(x, pdagum(x, shape1.a = shape1.a, shape2.p = 5), col = "green")
legend("bottomright", col = c("orange","blue","green"), lty = rep(1, len = 3),
       legend = paste("shape1.a =", shape1.a, ", shape2.p =", c(1, 2, 5)))