dmb {MBBEFDLite} | R Documentation |
The MBBEFD Distribution
Description
Density, distribution function, quantile function and random generation for the
MBBEFD distribution with parameters g
and b
.
Usage
dmb(x, g, b, c = NULL, log = FALSE)
pmb(q, g, b, c = NULL, lower.tail = TRUE, log.p = FALSE)
qmb(p, g, b, c = NULL, lower.tail = TRUE, log.p = FALSE)
rmb(n, g, b, c = NULL)
Arguments
x , q |
numeric; vector of quantiles. |
p |
numeric; vector of probabilities. |
n |
numeric; number of observations. If |
g |
numeric; (vector of) the |
b |
numeric; (vector of) the |
c |
numeric; (vector of) the optional |
log , log.p |
logical; if TRUE, probabilities p are given as log(p). |
lower.tail |
logical; if TRUE (default), probabilities are
|
Details
The MBBEFD class of curves are defined in Bernegger (1997) and are
often used to model insurance risk. The density is defined on the semi-open
interval [0, 1)
and the distribution and quantile functions are defined on
the closed interval [0, 1]
.
Value
dnorm
gives the density, pnorm
gives the distribution function,
qnorm
gives the quantile function, and rnorm
generates random
deviates.
The length of the result is determined by n
for rnorm
, and is the
length of x
, p
, or q
as appropriate for the other
functions.
Numerical arguments other than n
are recycled to the length of the
result. Logical arguments should be of length 1.
Note
This package follows Bernegger's convention that the density function does not exists at 1. This differs from the mbbefd package.
Author(s)
Avraham Adler Avraham.Adler@gmail.com
References
Bernegger, S. (1997) The Swiss Re Exposure Curves and the MBBEFD Distribution Class. ASTIN Bulletin 27(1), 99–111. doi:10.2143/AST.27.1.563208
See Also
mommb
for parameter estimation.
Examples
all.equal(dmb(0.5, 1, 0), 0)
dmb(0.2, 20, 5)
pmb(0.98, 25, 4)
qmb(0.98, 25, 4) == 1
all.equal(qmb(pmb(0.98, 25, 4), 25, 4), 0.98)
set.seed(45)
rmb(3, 4, 12)
set.seed(45)
rmb(99:101, 4, 12) # Should equal previous call