R: Test symmetry based on Lambert W heavy tail(s)

test_symmetry {LambertW} | R Documentation

## Test symmetry based on Lambert W heavy tail(s)

### Description

Performs a test for the null hypothesis of symmetry, H_0: δ_l = δ_r, versus the alternative of asymmetry. This can be done using a Wald test of the linear restriction H_0: δ_l - δ_r = 0 or a likelihood ratio test.

By default it uses `"Wald"` test since this only requires the Hessian of the `"hh"` Lambert W fit. The `"LR"` test requires the log-likelihood values for both MLEs (type `"h"` and `"hh"`) and thus takes longer to compute.

### Usage

    test_symmetry(LambertW.fit, method = c("Wald", "LR"))

### Arguments

`LambertW.fit` | an object of class `LambertW_fit` with `type = "hh"` or a numeric vector (observed data). If it is data, then an asymmetric Lambert W \times Gaussian distribution (`distname = "normal"`) with two tail parameters (`"hh"`) will be fit to the data internally and then used as the new `LambertW.fit`.
`method` | test methodology: `"Wald"` (default) or a likelihood ratio `"LR"` test

### Value

A list of class `"htest"` containing:

`statistic` | value of the test statistic,
`p.value` | p-value for the test,
`method` | character string describing the test,
`data.name` | a character string giving the name(s) of the data.

### Examples

    ## Not run:
    # skewed
    yy <- rLambertW(n = 500, theta = list(delta = c(0.1, 0.25), beta = c(2, 1)),
                    distname = "normal")
    fit.ml <- MLE_LambertW(yy, type = "hh", distname = "normal",
                           hessian = TRUE)
    summary(fit.ml)
    test_symmetry(fit.ml, "LR")
    test_symmetry(fit.ml, "Wald")

    # symmetric
    yy <- rLambertW(n = 500, theta = list(delta = c(0.2, 0.2), beta = c(2, 1)),
                    distname = "normal")
    fit.ml <- MLE_LambertW(yy, type = "hh", distname = "normal")
    summary(fit.ml)
    test_symmetry(fit.ml, "LR")
    test_symmetry(fit.ml, "Wald")

    ## End(Not run)

[Package LambertW version 0.6.7 Index]