| InverseExponential {actuar} | R Documentation |
Density function, distribution function, quantile function, random generation
raw moments and limited moments for the Inverse Exponential
distribution with parameter scale.
dinvexp(x, rate = 1, scale = 1/rate, log = FALSE) pinvexp(q, rate = 1, scale = 1/rate, lower.tail = TRUE, log.p = FALSE) qinvexp(p, rate = 1, scale = 1/rate, lower.tail = TRUE, log.p = FALSE) rinvexp(n, rate = 1, scale = 1/rate) minvexp(order, rate = 1, scale = 1/rate) levinvexp(limit, rate = 1, scale = 1/rate, order)
x, q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations. If length(n) > 1, the length is
taken to be the number required. |
scale |
parameter. Must be strictly positive. |
rate |
an alternative way to specify the scale. |
log, log.p |
logical; if TRUE, probabilities/densities
p are returned as log(p). |
lower.tail |
logical; if TRUE (default), probabilities are
P[X <= x], otherwise, P[X > x]. |
order |
order of the moment. |
limit |
limit of the loss variable. |
The Inverse Exponential distribution with parameter scale
= s has density:
f(x) = s exp(-s/x)/x^2
for x > 0 and s > 0.
The kth raw moment of the random variable X is E[X^k] and the kth limited moment at some limit d is E[min(X, d)^k].
For numerical evaluation purposes, levinvexp requires that
order < 1.
dinvexp gives the density,
pinvexp gives the distribution function,
qinvexp gives the quantile function,
rinvexp generates random deviates,
minvexp gives the kth raw moment, and
levinvexp calculates the kth limited moment.
Invalid arguments will result in return value NaN, with a warning.
Vincent Goulet vincent.goulet@act.ulaval.ca and Mathieu Pigeon
Klugman, S. A., Panjer, H. H. and Willmot, G. E. (2004), Loss Models, From Data to Decisions, Second Edition, Wiley.
exp(dinvexp(2, 2, log = TRUE)) p <- (1:10)/10 pinvexp(qinvexp(p, 2), 2) minvexp(0.5, 2)