shape1, shape2 and
scale.
dgenpareto(x, shape1, shape2, rate = 1, scale = 1/rate, log = FALSE)
pgenpareto(q, shape1, shape2, rate = 1, scale = 1/rate, lower.tail = TRUE, log.p = FALSE)
qgenpareto(p, shape1, shape2, rate = 1, scale = 1/rate, lower.tail = TRUE, log.p = FALSE)
rgenpareto(n, shape1, shape2, rate = 1, scale = 1/rate)
mgenpareto(order, shape1, shape2, rate = 1, scale = 1/rate)
levgenpareto(limit, shape1, shape2, rate = 1, scale = 1/rate, order = 1)length(n) > 1, the length is
taken to be the number required.TRUE, probabilities/densities
$p$ are returned as $log(p)$.TRUE (default), probabilities are
$P[X <= x]$,="" otherwise,="" $p[x=""> x]$.dgenpareto gives the density,
pgenpareto gives the distribution function,
qgenpareto gives the quantile function,
rgenpareto generates random deviates,
mgenpareto gives the $k$th raw moment, and
levgenpareto gives the $k$th moment of the limited loss
variable.Invalid arguments will result in return value NaN, with a warning.
shape1
$= a$, shape2 $= b$ and scale
$= s$ has density:
$$f(x) = \frac{\Gamma(\alpha + \tau)}{\Gamma(\alpha)\Gamma(\tau)}
\frac{\theta^\alpha x^{\tau - 1}}{%
(x + \theta)^{\alpha + \tau}}$$
for $x > 0$, $a > 0$, $b > 0$ and
$s > 0$.
(Here $Gamma(a)$ is the function implemented
by R's gamma() and defined in its help.)The Generalized Pareto is the distribution of the random variable $$\theta \left(\frac{X}{1 - X}\right),$$ where $X$ has a Beta distribution with parameters $a$ and $b$.
The Generalized Pareto distribution has the following special cases:
shape2 ==
1;
shape1 == 1.
exp(dgenpareto(3, 3, 4, 4, log = TRUE))
p <- (1:10)/10
pgenpareto(qgenpareto(p, 3, 3, 1), 3, 3, 1)
qgenpareto(.3, 3, 4, 4, lower.tail = FALSE)
mgenpareto(1, 3, 2, 1) ^ 2
levgenpareto(10, 3, 3, 3, order = 2)
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