shape and scale.dparalogis(x, shape, rate = 1, scale = 1/rate, log = FALSE)
pparalogis(q, shape, rate = 1, scale = 1/rate,
lower.tail = TRUE, log.p = FALSE)
qparalogis(p, shape, rate = 1, scale = 1/rate,
lower.tail = TRUE, log.p = FALSE)
rparalogis(n, shape, rate = 1, scale = 1/rate)
mparalogis(order, shape, rate = 1, scale = 1/rate)
levparalogis(limit, shape, 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
$P[X \le x]$, otherwise, $P[X > x]$.dparalogis gives the density,
pparalogis gives the distribution function,
qparalogis gives the quantile function,
rparalogis generates random deviates,
mparalogis gives the $k$th raw moment, and
levparalogis gives the $k$th moment of the limited loss
variable. Invalid arguments will result in return value NaN, with a warning.
shape $=
\alpha$ and scale $= \theta$ has density:
$$f(x) = \frac{\alpha^2 (x/\theta)^\alpha}{ x [1 + (x/\theta)^\alpha)^{\alpha + 1}}$$
for $x > 0$, $\alpha > 0$ and $\theta > 0$.The $k$th raw moment of the random variable $X$ is $E[X^k]$ and the $k$ limited moment at some limit $d$ is $E[\min(X, d)]$.
exp(dparalogis(2, 3, 4, log = TRUE))
p <- (1:10)/10
pparalogis(qparalogis(p, 2, 3), 2, 3)
mparalogis(2, 2, 3) - mparalogis(1, 2, 3)^2
levparalogis(10, 2, 3, order = 2)Run the code above in your browser using DataLab