mommb {MBBEFDLite}R Documentation

Method of Moments Parameter Estimation for the MBBEFD distribution.

Description

Attempts to find the best g and b parameters which are consistent with the first and second moments of the supplied data.

Usage

mommb(x, maxit = 100L, tol = .Machine$double.eps ^ 0.5, na.rm = TRUE)

Arguments

x

numeric; vector of observations between 0 and 1.

maxit

integer; maximum number of iterations.

tol

numeric; tolerance. If too tight, algorithm may fail. Defaults to the square root of .Machine$double.eps or roughly 1.49\times 10^{-8}.

na.rm

logical; if TRUE (default) NAs are removed. If FALSE and there are NAs, the algorithm will stop with an error.

Details

The algorithm is based on sections 4.1 and 4.2 of Bernegger (1997). With rare exceptions, the fitted g and b parameters must conform to:

\mu = \frac{\ln(gb)(1-b)}{\ln(b)(1-gb)}

where \mu is the empirical mean.

However, in step 2 of section 4.2, the p component is estimated as the difference between the numerical integration of x^2 f(x) and the empirical second moment per equation (4.3). This is converted to g by reciprocation, and convergence is tested by the difference between this “new” g and its prior value.

Value

Returns a list containing:

g

The fitted g parameter.

b

The fitted b parameter.

iter

The number of iterations used.

sqerr

The squared error between the empirical mean and the theoretical mean given the fitted g and b.

Note

Anecdotal evidence indicates that the results of this fitting algorithm can be volatile, especially with fewer than a few hundred observations.

Author(s)

Avraham Adler Avraham.Adler@gmail.com

References

Bernegger, S. (1997) The Swiss Re Exposure Curves and the MBBEFD Distribution Class. ASTIN Bulletin 27(1), 99–111. doi:10.2143/AST.27.1.563208

See Also

rmb for random variate generation.

Examples

set.seed(85L)
x <- rmb(1000, 25, 4)
mommb(x)

[Package MBBEFDLite version 0.0.1 Index]