dpqrmb: The MBBEFD Distribution

In MBBEFDLite: Statistical Functions for the Maxwell-Boltzmann-Bose-Einstein-Fermi-Dirac (MBBEFD) Family of Distributions

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 length(n) > 1, the length is taken to be the number required.
g	numeric; (vector of) the g parameter, which is also the reciprocal of the probability of a maximum loss.
b	numeric; (vector of) the b parameter.
c	numeric; (vector of) the optional single c parameter. Should be NULL if g and b are passed. Otherwise, g = e^{(0.78 + 0.12c)c} and b = e^{3.1 - 0.15(1+c)c}.
log, log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are P[X\leq x] otherwise P[X > x].

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]. The parameters must satisfy g \ge 1 and b \ge 0.

Value

dmb gives the density, pmb gives the distribution function, qmb gives the quantile function, and rmb generates random deviates.

The length of the result is determined by n for rmb, 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 exist at 1. This differs from the mbbefd package.

Author(s)

Avraham Adler [e-mail]

References

Bernegger, S. (1997) The Swiss Re Exposure Curves and the MBBEFD Distribution Class. ASTIN Bulletin 27(1), 99–111. \Sexpr[results=rd]{tools:::Rd_expr_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) # length(99:101) = 3, so generates same 3 values as above

MBBEFDLite documentation built on March 10, 2026, 9:07 a.m.