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 |
scale |
parameter. Must be strictly positive. |
rate |
an alternative way to specify the scale. |
log, log.p |
logical; if |
lower.tail |
logical; if |
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], k < 1, and the kth limited moment at some limit d is E[min(X, d)^k], all k.
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.
levinvexp
computes the limited expected value using
gammainc
from package expint.
The "distributions"
package vignette provides the
interrelations between the continuous size distributions in
actuar and the complete formulas underlying the above functions.
Vincent Goulet vincent.goulet@act.ulaval.ca and Mathieu Pigeon
Klugman, S. A., Panjer, H. H. and Willmot, G. E. (2012), Loss Models, From Data to Decisions, Fourth Edition, Wiley.
exp(dinvexp(2, 2, log = TRUE)) p <- (1:10)/10 pinvexp(qinvexp(p, 2), 2) minvexp(0.5, 2)