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

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
dmbbefd(x, a, b, log=FALSE, g)
pmbbefd(q, a, b, lower.tail = TRUE, log.p = FALSE, g)
qmbbefd(p, a, b, lower.tail = TRUE, log.p = FALSE, g)
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)

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].

Details

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

Value

A numeric value or a vector.

Author(s)

Giorgio Spedicato, Dutang Christophe

References

BERNEGGER, STEFAN. THE SWISS RE EXPOSURE CURVES AND THE MBBEFD DISTRIBUTION CLASS. Astin Bulletin (1997): 99.

See Also

swissRe, exposureCurve.

Examples

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
#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