shape.
dpareto1(x, shape, min, log = FALSE)
ppareto1(q, shape, min, lower.tail = TRUE, log.p = FALSE)
qpareto1(p, shape, min, lower.tail = TRUE, log.p = FALSE)
rpareto1(n, shape, min)
mpareto1(order, shape, min)
levpareto1(limit, shape, min, 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,="" $p[x=""> x]$.dpareto1 gives the density,
ppareto1 gives the distribution function,
qpareto1 gives the quantile function,
rpareto1 generates random deviates,
mpareto1 gives the $k$th raw moment, and
levpareto1 gives the $k$th moment of the limited loss
variable.Invalid arguments will result in return value NaN, with a warning.
shape
$= a$ has density:
$$f(x) = \frac{\alpha \theta^\alpha}{x^{\alpha + 1}}$$
for $x > b$, $a > 0$ and $b > 0$. Although there appears to be two parameters, only shape is a true
parameter. The value of min $= b$ must be set in
advance.
The $k$th raw moment of the random variable $X$ is $E[X^k]$, $k < shape$ and the $k$th limited moment at some limit $d$ is $E[min(X, d)^k]$, $x \ge min$.
exp(dpareto1(5, 3, 4, log = TRUE))
p <- (1:10)/10
ppareto1(qpareto1(p, 2, 3), 2, 3)
mpareto1(2, 3, 4) - mpareto(1, 3, 4) ^ 2
levpareto(10, 3, 4, order = 2)
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