LWest-methods {LambertW}R Documentation

Methods for output of LambertW estimators

Description

Useful information for estimate output (class LWest): parameter estimate widehat{theta}, standard errors, theoretical support, etc.; nice formating (print), and plots (see Details).

Usage

## S3 method for class 'LWest':
summary(object, ...)
## S3 method for class 'summary.LWest':
print(x, ...)
## S3 method for class 'LWest':
print(x, ...)
## S3 method for class 'LWest':
plot(x, QQ=FALSE, ...)

Arguments

object object of class LWest
x object of class LWest
QQ should a LambertW QQ plot be displayed? default FALSE
... further arguments passed to or from other methods.

Details

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

print.summary.LWest tries to be smart about formatting the coefficients, standard errors, etc. and additionally gives "significance stars".

plot.LWest plots a (1) histogram, (2) empirical density of the data y. These are compared to the theoretical Gaussian (or t) and Lambert W times Gaussian (or t) densities (3) implied by widehat{theta}.

Value

summary gives an object of class summary.LWest. A list containing

call function call
coefmat matrix with 4 columns: widehat{theta}, its standard errors, t-statistic, and corresponding (two-sided) p-values
distname input distribution; default: "normal", alternative "t"
n number of observations
data original data set (y)
input back-transformed data
support support of Y
data.range empirical data range
method estimation method
hessian Hessian at the optimum. Numerically obtained for method = "MLE"; for method = "IGMM" only an approximation, as it is a diagonal matrix derived from the asymptotic covariance matrix obtained by simulations.
p_1 Probability that one observation was caused by input lying on the non-principal branch; see p_1.
p_1n Probability that one or more of the n observation was caused by input lying on the non-principal branch; see p_1.

Author(s)

Georg M. Goerg

References

Goerg, G.M. (2009). “Lambert W Random Variables - A new class of skewed distribution functions”. Unpublished

Examples

data(AA)
attach(AA)

X=AA[AA$sex=="f",]
y=X$bmi

fit.ml=MLE_LambertW(y)
A=summary(fit.ml)
print(A)

plot(fit.ml)

[Package LambertW version 0.1.9 Index]