VGAM (version 1.1-8)

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, 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)

Value

ddagum gives the density,

pdagum gives the distribution function,

qdagum gives the quantile function, and

rdagum generates random deviates.

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.

Author

T. W. Yee and Kai Huang

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(probs, shape1.a = shape1.a, shape2.p =
  shape2.p), shape1.a = shape1.a, shape2.p = shape2.p) - probs))

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)))