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Lomax {Renext}

Lomax distribution
Package: 
Renext
Version: 
2.1-0

Description

Density function, distribution function, quantile function and random generation for the Lomax distribution.

Usage

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)

Arguments

x, q
Vector of quantiles.
p
Vector of probabilities.
n
Number of observations.
scale, shape
Shift and shape parameters. Vectors of length > 1 are not accepted.
log
Logical; if TRUE, the log density is returned.
lower.tail
Logical; if TRUE (default), probabilities are Pr[X <= x], otherwise, Pr[X > x].

Details

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 .

Values

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

References

Johnson N. Kotz S. and N. Balakrishnan Continuous Univariate Distributions vol. 1, Wiley 1994.

http://en.wikipedia.org/wiki/Lomax_distributionLomax distribution in Wikipedia

Note

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.

See Also

flomax to fit the Lomax distibution by Maximum Likelihood.

Examples

shape <- 5; scale <- 10
xl <- qlomax(c(0.00, 0.99), scale = scale, shape = shape)
x <- seq(from = xl[1], to = xl[2], 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")

Documentation reproduced from package Renext, version 2.1-0. License: GPL (>= 2)