gldFit {fBasics} | R Documentation

## GH Distribution Fit

### Description

Estimates the distrinbutional parameters for a generalized lambda distribution.

### Usage

    gldFit(x, lambda1 = 0, lambda2 = -1, lambda3 = -1/8, lambda4 = -1/8,
        method = c("mle", "mps", "gof", "hist", "rob"),
        scale = NA, doplot = TRUE, add = FALSE, span = "auto", trace = TRUE,
        title = NULL, description = NULL, ...)

### Arguments

`x` | a numeric vector.
`lambda1, lambda2, lambda3, lambda4` | are numeric values where `lambda1` is the location parameter, `lambda2` is the location parameter, `lambda3` is the first shape parameter, and `lambda4` is the second shape parameter.
`method` | a character string, the estimation approach to fit the distributional parameters, see details.
`scale` | not used.
`doplot` | a logical flag. Should a plot be displayed?
`add` | a logical flag. Should a new fit added to an existing plot?
`span` | 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 rigldt endpoints of the range, and `n` gives the number of the intermediate points.
`trace` | a logical flag. Should the parameter estimation process be traced?
`title` | a character string which allows for a project title.
`description` | a character string which allows for a brief description.
`...` | parameters to be parsed.

### Details

The function `nlminb` is used to minimize the objective function. The following approaches have been implemented:

`"mle"`, maximimum log likelihoo estimation.

`"mps"`, maximum product spacing estimation.

`"gof"`, goodness of fit approaches, `type="ad"` Anderson-Darling, `type="cvm"` Cramer-vonMise, `type="ks"` Kolmogorov-Smirnov.

`"hist"`, histogram binning approaches, `"fd"` Freedman-Diaconis binning, `"scott"`, Scott histogram binning, `"sturges"`, Sturges histogram binning.

`"rob"`, robust moment matching.

### Value

returns a list with the following components:

`estimate` | the point at which the maximum value of the log liklihood function is obtained.
`minimum` | the value of the estimated maximum, i.e. the value of the log liklihood function.

`code`

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.

`gradient` | the gradient at the estimated maximum.
`steps` | number of function calls.

### Examples

    ## gldFit -
       # Simulate Random Variates:
       set.seed(1953)
       s = rgld(n = 1000, lambda1=0, lambda2=-1, lambda3=-1/8, lambda4=-1/8)

    ## gldFit -
       # Fit Parameters:
       gldFit(s, lambda1=0, lambda2=-1, lambda3=-1/8, lambda4=-1/8,
         doplot = TRUE, trace = TRUE)

[Package fBasics version 3042.89 Index]