Maxlo {Renext} | R Documentation |
'maxlo' distribution
Description
Density function, distribution function, quantile function and random generation for the 'maxlo' distribution.
Usage
dmaxlo(x, scale = 1.0, shape = 4.0, log = FALSE)
pmaxlo(q, scale = 1.0, shape = 4.0, lower.tail = TRUE)
qmaxlo(p, scale = 1.0, shape = 4.0)
rmaxlo(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 |
lower.tail |
Logical; if |
Details
The 'maxlo' distribution function with shape and scale
is a special case of Generalised Pareto (GPD) with
negative shape
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
This distribution has a coefficient of variation smaller than .
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
where is the scale parameter of the
GPD. Since only GPD with
seem to be used in practice,
this distribution should be used with
.
This distribution can be used in POT to describe bounded excesses
following GPD with shape . The scale parameter
then represents the upper end-point of the excesses,
implying the finite upper end-point
for the levels,
where
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")