VGAM (version 1.0-4)

# Lomax: The Lomax Distribution

## Description

Density, distribution function, quantile function and random generation for the Lomax distribution with scale parameter `scale` and shape parameter `q`.

## Usage

```dlomax(x, scale = 1, shape3.q, log = FALSE)
plomax(q, scale = 1, shape3.q, lower.tail = TRUE, log.p = FALSE)
qlomax(p, scale = 1, shape3.q, lower.tail = TRUE, log.p = FALSE)
rlomax(n, scale = 1, shape3.q)```

## 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.

scale

scale parameter.

shape3.q

shape 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

`dlomax` gives the density, `plomax` gives the distribution function, `qlomax` gives the quantile function, and `rlomax` generates random deviates.

## Details

See `lomax`, 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.

`lomax`, `genbetaII`.

## Examples

Run this code
``````# NOT RUN {
probs <- seq(0.1, 0.9, by = 0.1)
max(abs(plomax(qlomax(p = probs, shape3.q =  1),
shape3.q = 1) - probs))  # Should be 0

# }
# NOT RUN {
par(mfrow = c(1, 2))
x <- seq(-0.01, 5, len = 401)
plot(x, dexp(x), type = "l", col = "black", ylab = "", ylim = c(0, 3),
main = "Black is standard exponential, others are dlomax(x, shape3.q)")
lines(x, dlomax(x, shape3.q = 1), col = "orange")
lines(x, dlomax(x, shape3.q = 2), col = "blue")
lines(x, dlomax(x, shape3.q = 5), col = "green")
legend("topright", col = c("orange","blue","green"), lty = rep(1, 3),
legend = paste("shape3.q =", c(1, 2, 5)))

plot(x, pexp(x), type = "l", col = "black", ylab = "", las = 1,
main = "Black is standard exponential, others are plomax(x, shape3.q)")
lines(x, plomax(x, shape3.q = 1), col = "orange")
lines(x, plomax(x, shape3.q = 2), col = "blue")
lines(x, plomax(x, shape3.q = 5), col = "green")
legend("bottomright", col = c("orange","blue","green"), lty = rep(1, 3),
legend = paste("shape3.q =", c(1, 2, 5)))
# }
``````

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