This function fits a dynamic mixture via standard maximum likelihood.
Currently only implemented for the lognormal - generalized Pareto case,
with Cauchy or exponential weight.
Usage
MLEfit(yObs, bootreps, intTol = 1e-04, weight)
Value
MLEpars vector: maximum likelihood estimates and maximized
log-likelihood.
MLEboot matrix: maximum likelihood estimates obtained in
each bootstrap replication.
sdMLE vector: bootstrap standard deviation of the MLEs.
Arguments
yObs
numerical vector: observed sample.
bootreps
non-negative integer: number of bootstrap replications. If equal to 0, no standard errors are computed.
intTol
non-negative scalar: threshold for stopping the computation of the integral in the normalization
constant: if the integral on the interval from n-1 to n is smaller than intTol, the approximation procedure stops.
weight
'cau' or 'exp': name of weight distribution.
Details
Starting values for \(\mu\) and \(\sigma\) are the lognormal MLEs computed
with the observations below the median. Initial values for \(\xi\) and
\(\tau\) are the GPD MLEs obtained with the observations above the median.
For the location and scale parameter of the Cauchy, we respectively use
the first quartile and abs(log(sd(x)/2)). For the parameter of the exponential, we use
abs(log(sd(x)/2)).