# test_symmetry: Test symmetry based on Lambert W heavy tail(s) In LambertW: Probabilistic Models to Analyze and Gaussianize Heavy-Tailed, Skewed Data

 test_symmetry 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)


LambertW documentation built on Sept. 22, 2022, 5:07 p.m.