Renext (version 2.0-0)

Lomax: Lomax distribution

Description

Density function, distribution function, quantile function and random generation for the Lomax distribution. 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 $\textrm{Pr}[X <= x]$,="" otherwise,="" $\textrm{pr}[x=""> x]$

Value

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

Details

The lomax distribution function with shape $\rho>0$ and scale $\delta>0$ has distribution function $$F(y) = 1- \left[\frac{\delta}{\delta+y}\right]^\rho \quad y>0$$ This distribution has increasing hazard and decreasing mean residual life (MRL). The coefficient of variation decreases with $\rho$ and tends to $1$ for large $\rho$. The default value $\rho=4$ corresponds to $CV = \sqrt{2}$.

References

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

Examples

library(Renext)
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")