IGMM {LambertW}R Documentation

Iterative Generalized Method of Moments – IGMM

Description

An iterative method finds this value of theta = (delta, μ_x, σ_x) which minimizes the distance between the sample and theoretical skewness of X. For details of the Algorithm see the References.

Usage

IGMM(y, tol = .Machine$double.eps^0.5, gamma_x = 0, theta.0=c((skewness(y)-gamma_x)/6, median(y), sd(y)), robust = FALSE)
## Default S3 method:
IGMM(y, tol = .Machine$double.eps^0.5, gamma_x = 0, theta.0=c((skewness(y)-gamma_x)/6, median(y), sd(y)), robust = FALSE)

Arguments

y a numeric vector of real values.
tol convergence tolerance (conversion reached); default: .Machine$double.eps^0.5
gamma_x theoretical skewness of input X; default 0
theta.0 starting values for IGMM algorithm; default: ((skewness(y)-gamma_x)/6, median(y), sd(y))
robust robust estimation of the sample skewness (see mc)? default FALSE

Value

An object of class LWest:

data the data y
theta IGMM estimate for theta
iterations number of iterations
call function call
message message from the optimization method. What kind of convergence?
distname a character string stating the theoretical skewness of the input distribution. Same information as gamma_x
gamma_x a-priori imposed theoretical skewness (numeric value); default: 0
method Estimation method. Here "IGMM"

Author(s)

Georg M. Goerg

References

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 Unpublished

Examples

x=rnorm(1000)
fit=IGMM(x)
summary(fit)

y=rLambertW(n=1000, c(0.1, 2,1))
fity=IGMM(y)
summary(fity)
plot(fity)

[Package LambertW version 0.1.9 Index]