mommb {MBBEFDLite} | R Documentation |
Attempts to find the best g
and b
parameters which are consistent
with the first and second moments of the supplied data.
mommb(x, maxit = 100L, tol = .Machine$double.eps ^ 0.5, na.rm = TRUE)
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 TRUE (default) |
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.
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 |
Anecdotal evidence indicates that the results of this fitting algorithm can be volatile, especially with fewer than a few hundred observations.
Avraham Adler Avraham.Adler@gmail.com
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
rmb
for random variate generation.
set.seed(85L)
x <- rmb(1000, 25, 4)
mommb(x)