mbbefd-distr: The MBBEFD distribution (two parametrizations)

Description

These functions perform probabilistic analysis as well as random sampling on the MBBEFD distribution: the 1st parametrization MBBEFD(a,b) is implemented in <d,p,q,r>mbbefd, the 2nd parametrization MBBEFD(g,b) is implemented in <d,p,q,r>MBBEFD. We also provide raw moments, exposure curve function and total loss.

Usage

dmbbefd(x, a, b, log=FALSE)
pmbbefd(q, a, b, lower.tail = TRUE, log.p = FALSE)
qmbbefd(p, a, b, lower.tail = TRUE, log.p = FALSE)
rmbbefd(n, a, b)
ecmbbefd(x, a, b)
mmbbefd(order, a, b)
tlmbbefd(a, b)
dMBBEFD(x, g, b, log=FALSE)
pMBBEFD(q, g, b, lower.tail = TRUE, log.p = FALSE)
qMBBEFD(p, g, b, lower.tail = TRUE, log.p = FALSE)
rMBBEFD(n, g, b)
ecMBBEFD(x, g, b)
mMBBEFD(order, g, b)
tlMBBEFD(g, b)

Value

A numeric value or a vector.

Arguments

x, q: vector of quantiles.
p: vector of probabilities.
n: number of observations. If length(n) > 1, the length is take to be the number required.
a, b, g: shape parameters. For .mbbefd functions, g is computed from a.
order: order of the raw moment.
log, log.p: logical; if TRUE, probabilities p are given as log(p).
lower.tail: logical; if TRUE (default), probabilities are \(P[X <= x]\), otherwise, \(P[X> x]\).

Author

Giorgio Spedicato, Dutang Christophe

Details

it shall be remebered that \(g=\frac{1}{p_1}=\frac{a+b}{\left(a+1\right)*b}\).

References

BERNEGGER, STEFAN (1997). The Swiss Re Exposure Curves And The MBBEFD Distribution Class, ASTIN Bulletin, 27(1), pp99-111, tools:::Rd_expr_doi("https://doi.org/10.2143/AST.27.1.563208").

Examples

Run this code

#1st parametrization
#
aPar=0.2
bPar=0.04
rmbbefd(n=10,a=aPar,b=bPar) #for random generation
qmbbefd(p=0.7,a=aPar,b=bPar) #for quantiles
dmbbefd(x=0.5,a=aPar,b=bPar) #for density
pmbbefd(q=0.5,a=aPar,b=bPar) #for distribution function

#2nd parametrization
#
gPar=2
bPar=0.04
rMBBEFD(n=10,g=gPar,b=bPar) #for random generation
qMBBEFD(p=0.7,g=gPar,b=bPar) #for quantiles
dMBBEFD(x=0.5,g=gPar,b=bPar) #for density
pMBBEFD(q=0.5,g=gPar,b=bPar) #for distribution function

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