R: Methods for Lambert W\times F estimates

LambertW_fit-methods {LambertW} | R Documentation

## Methods for Lambert W\times F estimates

### Description

S3 methods (`print`, `plot`, `summary`, etc.) for `LambertW_fit` class returned by the `MLE_LambertW` or `IGMM` estimators.

`plot.LambertW_fit` plots a (1) histogram, (2) empirical density of the data `y`. These are compared (3) to the theoretical F_X(x \mid \widehat{\boldsymbol β}) and (4) Lambert W \times F_X(y \mid \widehat{\boldsymbol β}) densities.

`print.LambertW_fit` prints only very basic information about \widehat{θ} (to prevent an overload of data/information in the console when executing an estimator).

`print.summary.LambertW_fit` tries to be smart about formatting the coefficients, standard errors, etc. and also displays "significance stars" (like in the output of `summary.lm`).

`summary.LambertW_fit` computes some auxiliary results from the estimate such as standard errors, theoretical support (only for `type="s"`), skewness tests (only for `type="hh"`), etc. See `print.summary.LambertW_fit` for print out in the console.

### Usage

    ## S3 method for class 'LambertW_fit'
    plot(x, xlim = NULL, show.qqplot = FALSE, ...)

    ## S3 method for class 'LambertW_fit'
    print(x, ...)

    ## S3 method for class 'summary.LambertW_fit'
    print(x, ...)

    ## S3 method for class 'LambertW_fit'
    summary(object, ...)

### Arguments

`x, object` | object of class `LambertW_fit`
`xlim` | lower and upper limit of x-axis for cdf and pdf plots.
`show.qqplot` | should a Lambert W \times F QQ plot be displayed? Default: `FALSE`.
`...` | further arguments passed to or from other methods.

### Value

`summary` returns a list of class `summary.LambertW_fit` containing

`call` | function call
`coefmat` | matrix with 4 columns: \widehat{θ}, its standard errors, t-statistic, and two-sided p-values
`distname` | see Arguments
`n` | number of observations
`data` | original data (`y`)
`input` | back-transformed input data
`support` | support of output random variable Y
`data.range` | empirical data range
`method` | estimation method
`hessian` | Hessian at the optimum. Numerically obtained for `method = "MLE"`; for `method = "IGMM"` a diagonal-matrix approximation from covariance matrix obtained by simulations for n = 1000 samples in Goerg (2011).
`p_m1, p_m1n` | Probability that one (or n) observation were caused by input from the non-principal branch (see `p_m1`); only for `type = "s"`.
`symmetry.p.value` | p-value from Wald test of identical left and right tail parameters (see `test_symmetry`); only for `type = "hh"`.

### Examples

    # See ?LambertW-package

[Package LambertW version 0.6.7 Index]