# mbbefdDistribution: The MBBEFD distribution (two parametrizations) In mbbefd: Maxwell Boltzmann Bose Einstein Fermi Dirac Distribution and Destruction Rate Modelling

## 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.

swissRe, exposureCurve.
  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