R: The Dagum Distribution

Dagum {VGAM} | R Documentation

## 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)

### 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`.

### Details

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

### Value

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

### Note

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

### Author(s)

T. W. Yee and Kai Huang

### 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))

    ## Not run:  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)))

    ## End(Not run)

[Package VGAM version 1.1-3 Index]