IGMM {LambertW} | R Documentation |
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.
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)
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 |
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" |
Georg M. Goerg
Goerg, G.M. (2009). “Lambert W Random Variables - A new class of skewed distribution functions”. Unpublished
x=rnorm(1000) fit=IGMM(x) summary(fit) y=rLambertW(n=1000, c(0.1, 2,1)) fity=IGMM(y) summary(fity) plot(fity)