shape and scale.
dinvparalogis(x, shape, rate = 1, scale = 1/rate, log = FALSE)
pinvparalogis(q, shape, rate = 1, scale = 1/rate, lower.tail = TRUE, log.p = FALSE)
qinvparalogis(p, shape, rate = 1, scale = 1/rate, lower.tail = TRUE, log.p = FALSE)
rinvparalogis(n, shape, rate = 1, scale = 1/rate)
minvparalogis(order, shape, rate = 1, scale = 1/rate)
levinvparalogis(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
$P[X <= x]$,="" otherwise,="" $p[x=""> x]$.dinvparalogis gives the density,
pinvparalogis gives the distribution function,
qinvparalogis gives the quantile function,
rinvparalogis generates random deviates,
minvparalogis gives the $k$th raw moment, and
levinvparalogis gives the $k$th moment of the limited loss
variable.Invalid arguments will result in return value NaN, with a warning.
shape
$= a$ and scale $= s$ has density:
$$f(x) = \frac{\tau^2 (x/\theta)^{\tau^2}}{%
x [1 + (x/\theta)^\tau]^{\tau + 1}}$$
for $x > 0$, $a > 0$ and $b > 0$.The $k$th raw moment of the random variable $X$ is $E[X^k]$ and the $k$th limited moment at some limit $d$ is $E[min(X, d)^k]$.
exp(dinvparalogis(2, 3, 4, log = TRUE))
p <- (1:10)/10
pinvparalogis(qinvparalogis(p, 2, 3), 2, 3)
minvparalogis(-1, 2, 2)
levinvparalogis(10, 2, 2, order = 1)
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