Estimates the distrinbutional parameters for a generalized hyperbolic distribution.
ghFit(x, alpha = 1, beta = 0, delta = 1, mu = 0, lambda = -1/2,
scale = TRUE, doplot = TRUE, span = "auto", trace = TRUE,
title = NULL, description = NULL, ...)returns a list with the following components:
the point at which the maximum value of the log liklihood function is obtained.
the value of the estimated maximum, i.e. the value of the log liklihood function.
an integer indicating why the optimization process terminated.
1: relative gradient is close to zero, current iterate is probably
solution;
2: successive iterates within tolerance, current iterate is probably
solution;
3: last global step failed to locate a point lower than estimate.
Either estimate is an approximate local minimum of the
function or steptol is too small;
4: iteration limit exceeded;
5: maximum step size stepmax exceeded five consecutive times.
Either the function is unbounded below, becomes asymptotic to a
finite value from above in some direction or stepmax
is too small.
the gradient at the estimated maximum.
number of function calls.
a numeric vector.
The parameters are alpha, beta, delta,
mu, and and lambda:
shape parameter alpha;
skewness parameter beta, abs(beta) is in the
range (0, alpha);
scale parameter delta, delta must be zero or
positive;
location parameter mu, by default 0;
and lambda parameter lambda, by default -1/2.
a logical flag, by default TRUE. Should the time series
be scaled by its standard deviation to achieve a more stable
optimization?
a logical flag. Should a plot be displayed?
x-coordinates for the plot, by default 100 values
automatically selected and ranging between the 0.001,
and 0.999 quantiles. Alternatively, you can specify
the range by an expression like span=seq(min, max,
times = n), where, min and max are the
left and right endpoints of the range, and n gives
the number of the intermediate points.
a logical flag. Should the parameter estimation process be traced?
a character string which allows for a project title.
a character string which allows for a brief description.
parameters to be parsed.
The function nlm is used to minimize the "negative"
maximum log-likelihood function. nlm carries out a minimization
using a Newton-type algorithm.
## ghFit -
# Simulate Random Variates:
set.seed(1953)
s = rgh(n = 1000, alpha = 1.5, beta = 0.3, delta = 0.5, mu = -1.0)
## ghFit -
# Fit Parameters:
ghFit(s, alpha = 1, beta = 0, delta = 1, mu = mean(s), doplot = TRUE)
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