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 'maxlo' distribution function with shape α>0 and scale
β>0 is a special case of Generalised Pareto (GPD) with
negative shapeξ < 0 and location at zero. This is the
finite upper endpoint case of the GPD. Its name is nonstandard and was
chosen to suggest some form of symmetry with respect to the Lomax
distribution.
The survival function is
S(y) = [1 - y / β]^α (0 < y < β)
This distribution has a coefficient of variation smaller than 1.
Value
dmaxlo gives the density function, pmaxlo gives the
distribution function, qmaxlo gives the quantile function, and
rmaxlo generates random deviates.
Note
The 'maxlo' and GPD parameters are related according to
α = -1/ξ, β =
-σ/ξ.
where σ is the scale parameter of the
GPD. Since only GPD with ξ > -0.5 seem to be used in practice,
this distribution should be used with α > 2.
This distribution can be used in POT to describe bounded excesses
following GPD with shape ξ < 0. The scale parameter
β then represents the upper end-point of the excesses,
implying the finite upper end-point u + β for the levels,
where u is the threshold. It can be used in Renouv
with a fixed scale parameter, thus allowing a control of the upper
end-point.
This distribution is simply a rescaled version of a beta distribution
and also a rescaled version of a Kumaraswamy distribution. The name
"maxlo" is used here to suggest a form of symmetry to Lomax
distribution.
See Also
fmaxlo to fit such a distribution by Maximum Likelihood.
Examples
xs <- rmaxlo(500, shape = 2.2, scale = 1000)
hist(xs, main = "'maxlo' distribution"); rug(xs)
xs <- rmaxlo(500, shape = 4, scale = 1000)
hist(xs, main = "'maxlo' distribution"); rug(xs)
x <- seq(from = -10, to = 1010, by = 2)
plot(x = x, y = dmaxlo(x, shape = 4, scale = 1000),
type = "l", ylab = "dens",
col = "orangered", main = "dmaxlo and dgpd")
abline(h = 0)
lines(x = x, y = dgpd(x, shape = -1/4, scale = 250),
type = "l",
col = "SpringGreen3", lty = "dashed")
Results
R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)
R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.
R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.
Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.
> library(Renext)
Loading required package: evd
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/Renext/Maxlo.Rd_%03d_medium.png", width=480, height=480)
> ### Name: Maxlo
> ### Title: 'maxlo' distribution
> ### Aliases: Maxlo dmaxlo pmaxlo qmaxlo rmaxlo
> ### Keywords: distribution
>
> ### ** Examples
>
> xs <- rmaxlo(500, shape = 2.2, scale = 1000)
> hist(xs, main = "'maxlo' distribution"); rug(xs)
>
> xs <- rmaxlo(500, shape = 4, scale = 1000)
> hist(xs, main = "'maxlo' distribution"); rug(xs)
>
> x <- seq(from = -10, to = 1010, by = 2)
> plot(x = x, y = dmaxlo(x, shape = 4, scale = 1000),
+ type = "l", ylab = "dens",
+ col = "orangered", main = "dmaxlo and dgpd")
> abline(h = 0)
> lines(x = x, y = dgpd(x, shape = -1/4, scale = 250),
+ type = "l",
+ col = "SpringGreen3", lty = "dashed")
>
>
>
>
>
>
>
>
> dev.off()
null device
1
>