mbbefdDistribution: The MBBEFD distribution (two parametrizations)

In spedygiorgio/mbbefd: Maxwell Boltzmann Bose Einstein Fermi Dirac Distribution and Destruction Rate Modelling

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)

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}{\left(a+1\right)*b}.

Value

A numeric value or a vector.

Author(s)

Giorgio Spedicato, Dutang Christophe

References

BERNEGGER, STEFAN (1997). The Swiss Re Exposure Curves And The MBBEFD Distribution Class, ASTIN Bulletin, 27(1), pp99-111, \Sexpr[results=rd]{tools:::Rd_expr_doi("https://doi.org/10.2143/AST.27.1.563208")}.

See Also

swissRe, exposureCurve.

Examples

#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

spedygiorgio/mbbefd documentation built on Sept. 2, 2023, 1:55 p.m.