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
$P[X \le x]$, 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
$= \tau$ and scale $= \theta$ has density:
$$f(x) = \frac{\tau^2 (x/\theta)^{\tau^2}}{ x [1 + (x/\theta)^\tau]^{\tau + 1}}$$
for $x > 0$, $\tau > 0$ and $\theta > 0$.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)Run the code above in your browser using DataLab