Density function, distribution function, quantile function and random generation for the Lomax distribution.
dlomax(x, scale = 1.0, shape = 4.0, log = FALSE) plomax(q, scale = 1.0, shape = 4.0, lower.tail = FALSE) qlomax(p, scale = 1.0, shape = 4.0) rlomax(n, scale = 1.0, shape = 4.0)
- x, q
- Vector of quantiles.
- Vector of probabilities.
- Number of observations.
- scale, shape
- Shift and shape parameters. Vectors of length > 1 are not accepted.
- Logical; if
TRUE, the log density is returned.
- Logical; if
TRUE(default), probabilities are Pr[X <= x], otherwise, Pr[X > x].
The Lomax distribution function with shape α > 0 and scale β > 0 has survival function This distribution has increasing hazard and decreasing mean residual life (MRL). The coefficient of variation decreases with α, and tends to 1 for large α. The default value α=4 corresponds to .
dlomax gives the density function,
plomax gives the distribution function,
qlomax gives the quantile function, and
rlomax generates random deviates.
Johnson N. Kotz S. and N. Balakrishnan Continuous Univariate Distributions vol. 1, Wiley 1994.
http://en.wikipedia.org/wiki/Lomax_distributionLomax distribution in Wikipedia
This distribution is sometimes called log-exponential. It is a special case of Generalised Pareto Distibution (GPD) whith positive shape ξ > 0, scale σ and location μ=0. The Lomax and GPD parameters are related according to α = 1/ξ, β = σ/ξ. The Lomax distribution can be used in POT to describe exceedances following GPD with shape ξ>0 thus with decreasing hazard and increasing Mean Residual Life. Note that the exponential distribution with rate ν is the limit of a Lomax distibution having large scale β and large shape α, with the constraint on the shape/scale ratio α/β = ν.
flomax to fit the Lomax distibution by Maximum Likelihood.
shape <- 5; scale <- 10 xl <- qlomax(c(0.00, 0.99), scale = scale, shape = shape) x <- seq(from = xl, to = xl, length.out = 200) f <- dlomax(x, scale = scale, shape = shape) plot(x, f, type = "l", main = "Lomax distribution density") F <- plomax(x, scale = scale, shape = shape) plot(x, F, type ="l", main ="Lomax distribution function")
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