# glogisfit

##### Fitting the Generalized Logistic Distribution

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

- Keywords
- regression

##### Usage

```
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, …)

##### Arguments

- x
- 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
- 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.

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).

##### 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

##### Examples

```
# 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
# }
```

*Documentation reproduced from package glogis, version 1.0-1, License: GPL-2 | GPL-3*