InverseExponential {actuar} | R Documentation |
Density, 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 = 1)
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.
Invalid arguments will result in return value NaN
, with a warning.
The kth 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)].
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(-2, order = 3)