The Dagum Distribution

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

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

lower.tail, log.p

Same meaning as in pnorm or qnorm.

Value

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

References

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

Author

T. W. Yee and Kai Huang

Details

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

Note

The Dagum distribution is a special case of the 4-parameter generalized beta II distribution.

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(probs, shape1.a = shape1.a, shape2.p =
  shape2.p), shape1.a = shape1.a, shape2.p = shape2.p) - probs))
#> [1] 5.551115e-17

if (FALSE)  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 std 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 std 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)))

 # \dontrun{}