VGAM (version 1.1-12)

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)

Value

dlomax gives the density,

plomax gives the distribution function,

qlomax gives the quantile function, and

rlomax 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.

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.

Author

T. W. Yee and Kai Huang

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.

See Also

lomax, genbetaII.

Examples

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

if (FALSE)  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 std 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 std 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)))