# 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.

`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)