Fit a univariate generalized logisitc distribution (Type I: skew-logistic with location, scale, and shape parameters) to a sample of observations.
glogisfit(x, …)
# S3 method for default
glogisfit(x, weights = NULL, start = NULL, fixed = c(NA, NA, NA),
method = "BFGS", hessian = TRUE, …)
# S3 method for formula
glogisfit(formula, data, subset, na.action, weights, x = TRUE, …)# S3 method for glogisfit
plot(x, main = "", xlab = NULL, fill = "lightgray",
col = "blue", lwd = 1, lty = 1, xlim = NULL, ylim = NULL,
legend = "topright", moments = FALSE, …)
# S3 method for glogisfit
summary(object, log = TRUE, breaks = NULL, …)
# S3 method for glogisfit
coef(object, log = TRUE, …)
# S3 method for glogisfit
vcov(object, log = TRUE, …)
optional numeric vector of weights.
optional vector of starting values. The parametrization has to be
in terms of location, log(scale), log(shape) where the
original parameters (without logs) are as in dglogis. Default
is to use c(0, 0, 0) (i.e., standard logistic). For details see below.
specification of fixed parameters (see description of start).
NA signals that the corresponding parameter should be estimated.
A standard logistic distribution could thus be fitted via fixed = c(NA, NA, 0).
character string specifying optimization method, see optim
for the available options. Further options can be passed to optim through
....
logical. Should the Hessian be used to compute the variance/covariance
matrix? If FALSE, no covariances or standard errors will be available in
subsequent computations.
symbolic description of the model, currently only x ~ 1 is
supported.
arguments controlling formula processing
via model.frame.
logical or character specification where to place a legend.
legend = FALSE suppresses the legend.
See legend for the character specification.
logical. If a legend is produced, it can either show the parameter
estimates (moments = FALSE, default) or the implied moments of the
distribution.
a fitted glogisfit object.
logical option in some extractor methods indicating whether scale and shape parameters should be reported in logs (default) or the original levels.
interval breaks for the chi-squared goodness-of-fit test. Either a numeric vector of two or more cutpoints or a single number (greater than or equal to 2) giving the number of intervals.
arguments passed to methods.
glogisfit returns an object of class "glogisfit", i.e., a list with components as follows.
estimated parameters from the model (with scale/shape in logs, if included),
associated estimated covariance matrix,
log-likelihood of the fitted model,
number of estimated parameters,
number of observations,
number of observations with non-zero weights,
the weights used (if any),
output from the optim call for maximizing the log-likelihood,
the method argument passed to the optim call,
the full set of model parameters (location/scale/shape), including estimated and fixed parameters, all in original levels (without logs),
associated mean/variance/skewness,
the starting values for the parameters passed to the optim call,
the original specification of fixed parameters,
the original function call,
the original data,
logical indicating successful convergence of optim,
the terms objects for the model (if the formula method was used).
glogisfit estimates the generalized logistic distribution (Type I: skew-logistic)
as given by dglogis. Optimization is performed numerically by
optim using analytical gradients. For obtaining numerically more
stable results the scale and shape parameters are specified in logs. Starting values
are chosen as c(0, 0, 0), i.e., corresponding to a standard (symmetric) logistic
distribution. If these fail, better starting values are obtained by running a Nelder-Mead
optimization on the original problem (without logs) first.
A large list of standard extractor methods is supplied to conveniently compute
with the fitted objects, including methods to the generic functions
print, summary, plot
(reusing hist and lines), coef,
vcov, logLik, residuals,
and estfun and
bread (from the sandwich package).
The methods for coef, vcov, summary, and bread report computations
pertaining to the scale/shape parameters in logs by default, but allow for switching back to
the original levels (employing the delta method).
Visualization employs a histogramm of the original data along with lines for the estimated density.
Further structural change methods for "glogisfit" objects are described in
breakpoints.glogisfit.
Shao Q (2002). Maximum Likelihood Estimation for Generalised Logistic Distributions. Communications in Statistics -- Theory and Methods, 31(10), 1687--1700.
Windberger T, Zeileis A (2014). Structural Breaks in Inflation Dynamics within the European Monetary Union. Eastern European Economics, 52(3), 66--88.
# NOT RUN {
## simple artificial example
set.seed(2)
x <- rglogis(1000, -1, scale = 0.5, shape = 3)
gf <- glogisfit(x)
plot(gf)
summary(gf)
## query parameters and associated moments
coef(gf)
coef(gf, log = FALSE)
gf$parameters
gf$moments
# }
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