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.
# 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, ...)
summary returns a list of class summary.LambertW_fit
containing
function call
matrix with 4 columns: \(\widehat{\theta}\), its standard errors, t-statistic, and two-sided p-values
see Arguments
number of observations
original data (y)
back-transformed input data
support of output random variable Y
empirical data range
estimation method
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).
Probability that one (or n) observation were caused by input
from the non-principal branch (see p_m1); only for type = "s".
p-value from Wald test of identical left and right tail parameters (see
test_symmetry); only for type = "hh".
object of class LambertW_fit
lower and upper limit of x-axis for cdf and pdf plots.
should a Lambert W\( \times\) F QQ plot be displayed? Default: FALSE.
further arguments passed to or from other methods.