dagumUC: The Dagum Distribution In VGAM: Vector Generalized Linear and Additive Models

Description

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

Usage

 ```1 2 3 4``` ```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.

`dagum`, `genbetaII`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25``` ```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) ```