glogisfit {glogis}

Fitting the Generalized Logistic Distribution

Description

Fit a univariate generalized logisitc distribution (Type I: skew-logistic with location, scale, and shape parameters) to a sample of observations.

Usage

glogisfit(x, ...)
## Default S3 method:
glogisfit(x, weights = NULL, start = NULL, fixed = c(NA, NA, NA),
  method = "BFGS", hessian = TRUE, ...)
## S3 method for class 'formula'
glogisfit(formula, data, subset, na.action, weights, x = TRUE, ...)

## S3 method for class '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 class 'glogisfit'
summary(object, log = TRUE, breaks = NULL, ...)
## S3 method for class 'glogisfit'
coef(object, log = TRUE, ...)
## S3 method for class 'glogisfit'
vcov(object, log = TRUE, ...)

Arguments

x

a vector of observation (may be a ts or zoo time series).

weights

optional numeric vector of weights.

start

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.

fixed

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).

method

character string specifying optimization method, see optim for the available options. Further options can be passed to optim through ....

hessian

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.

formula

symbolic description of the model, currently only x ~ 1 is supported.

data, subset, na.action

arguments controlling formula processing via model.frame.

main, xlab, fill, col, lwd, lty, xlim, ylim

standard graphical parameters, see plot and par.

legend

logical or character specification where to place a legend. legend = FALSE suppresses the legend. See legend for the character specification.

moments

logical. If a legend is produced, it can either show the parameter estimates (moments = FALSE, default) or the implied moments of the distribution.

object

a fitted glogisfit object.

log

logical option in some extractor methods indicating whether scale and shape parameters should be reported in logs (default) or the original levels.

breaks

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.

Details

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.

Value

glogisfit returns an object of class "glogisfit", i.e., a list with components as follows.

coefficients

estimated parameters from the model (with scale/shape in logs, if included),

vcov

associated estimated covariance matrix,

loglik

log-likelihood of the fitted model,

df

number of estimated parameters,

n

number of observations,

nobs

number of observations with non-zero weights,

weights

the weights used (if any),

optim

output from the optim call for maximizing the log-likelihood,

method

the method argument passed to the optim call,

parameters

the full set of model parameters (location/scale/shape), including estimated and fixed parameters, all in original levels (without logs),

moments

associated mean/variance/skewness,

start

the starting values for the parameters passed to the optim call,

fixed

the original specification of fixed parameters,

call

the original function call,

x

the original data,

converged

logical indicating successful convergence of optim,

terms

the terms objects for the model (if the formula method was used).

References

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.

See Also

dglogis, dlogis, breakpoints.glogisfit

Examples

## 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