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 |
na.rm |
logical; if |
Details
The algorithm is based on sections 4.1 and 4.2 of Bernegger (1997). With rare
exceptions, the fitted and
parameters must conform to:
subject to:
where and
are the “true” first and second moments
and
is the empirical second moment.
The algorithm starts with the estimate as an upper bound.
However, in step 2 of section 4.2, the
component is estimated as the
difference between the numerical integration of
and the empirical
second moment—
—as seen in equation (4.3).
This is converted to
by reciprocation and convergence is tested by the
difference between this new
and its prior value. If the new
, the algorithm attempts to restart with a larger
—a
smaller
. In this case, the algorithm tends to fail to converge.
Value
Returns a list containing:
g |
The fitted |
b |
The fitted |
iter |
The number of iterations used. |
sqerr |
The squared error between the empirical mean and the
theoretical mean given the fitted |
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)