LambertW (version 0.6.4)

LambertW_fit-methods: 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 \(F_X(x \mid \widehat{\boldsymbol \beta})\) and (4) Lambert W \(\times\) \(F_X(y \mid \widehat{\boldsymbol \beta})\) densities.

print.LambertW_fit prints only very basic information about \(\widehat{\theta}\) (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 LambertW_fit
plot(x, xlim = NULL, show.qqplot = FALSE, ...)
# S3 method for LambertW_fit
print(x, ...)
# S3 method for summary.LambertW_fit
print(x, ...)
# S3 method for 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: \(\widehat{\theta}\), 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

# NOT RUN {
# See ?LambertW-package

# }