ecmb | R Documentation |
Returns the limited average severity at x
of a random variable with an
MBBEFD distribution with parameters g
and b
.
ecmb(x, g, b, c = NULL, lower.tail = TRUE)
x |
numeric; vector of quantiles. |
g |
numeric; (vector of) the |
b |
numeric; (vector of) the |
c |
numeric; (vector of) the optional |
lower.tail |
logical; if TRUE (default), percentages are of the
total loss being less than or equal to |
Given random variable X
with an MBBEFD distribution with
parameters g
and b
, the exposure curve is defined as the
ratio of the limited average severity (LAS) of the variable at x
divided by the unlimited expected severity of the distribution:
LAS(x) = \frac{E(X\wedge x)}{E(X)}=\frac{\int_0^x t f(t) dt +
x \int_x^\infty f(t) dt }{\int_0^\infty t f(t) dt}
If one considers x
as a policy limit, then the value of
ecmb(x, g, b)
is the percentage of the total expected loss which will be
contained within the (reinsurance) policy limit. If lower.tail
is
FALSE
, the return value is the percentage of total loss which will exceed
the limit.
A numeric vector containing the values of the exposure curve for the passed
x
, b
, and g
vectors. If lower.tail
is FALSE
,
the return value is the complement of the exposure curve.
Avraham Adler Avraham.Adler@gmail.com
Bernegger, S. (1997) The Swiss Re Exposure Curves and the MBBEFD Distribution Class. ASTIN Bulletin 27(1), 99–111. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.2143/AST.27.1.563208")}
dmb
and pmb
for the density and distribution.
all.equal(ecmb(c(0, 1), 20, 5), c(0, 1))
ecmb(0.25, 100, 34)
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