MLE_LambertW: Maximum Likelihood Estimation for Lambert W \times F...

View source: R/MLE_LambertW.R

MLE_LambertWR Documentation

Maximum Likelihood Estimation for Lambert W \times F distributions

Description

Maximum Likelihood Estimation (MLE) for Lambert W \times F distributions computes \widehat{θ}_{MLE}.

For type = "s", the skewness parameter γ is estimated and δ = 0 is held fixed; for type = "h" the one-dimensional δ is estimated and γ = 0 is held fixed; and for type = "hh" the 2-dimensional δ is estimated and γ = 0 is held fixed.

By default α = 1 is fixed for any type. If you want to also estimate α (for type = "h" or "hh") set theta.fixed = list().

Usage

MLE_LambertW(
  y,
  distname,
  type = c("h", "s", "hh"),
  theta.fixed = list(alpha = 1),
  use.mean.variance = TRUE,
  theta.init = get_initial_theta(y, distname = distname, type = type, theta.fixed =
    theta.fixed, use.mean.variance = use.mean.variance, method = "IGMM"),
  hessian = TRUE,
  return.estimate.only = FALSE,
  optim.fct = c("optim", "nlm", "solnp"),
  not.negative = FALSE
)

Arguments

y

a numeric vector of real values.

distname

character; name of input distribution; see get_distnames.

type

type of Lambert W \times F distribution: skewed "s"; heavy-tail "h"; or skewed heavy-tail "hh".

theta.fixed

a list of fixed parameters in the optimization; default only alpha = 1.

use.mean.variance

logical; if TRUE it uses mean and variance implied by \boldsymbol β to do the transformation (Goerg 2011). If FALSE, it uses the alternative definition from Goerg (2016) with location and scale parameter.

theta.init

a list containing the starting values of (α, \boldsymbol β, γ, δ) for the numerical optimization; default: see get_initial_theta.

hessian

indicator for returning the (numerically obtained) Hessian at the optimum; default: TRUE. If the numDeriv package is available it uses numDeriv::hessian(); otherwise stats::optim(..., hessian = TRUE).

return.estimate.only

logical; if TRUE, only a named flattened vector of \widehat{θ}_{MLE} will be returned (only the estimated, non-fixed values). This is useful for simulations where it is usually not necessary to give a nicely organized output, but only the estimated parameter. Default: FALSE.

optim.fct

character; which R optimization function should be used. Either 'optim' (default), 'nlm', or 'solnp' from the Rsolnp package (if available). Note that if 'nlm' is used, then not.negative = TRUE will be set automatically.

not.negative

logical; if TRUE, it restricts delta or gamma to the non-negative reals. See theta2unbounded for details.

Value

A list of class LambertW_fit:

data

data y,

loglik

scalar; log-likelihood evaluated at the optimum \widehat{θ}_{MLE},

theta.init

list; starting values for numerical optimization,

beta

estimated \boldsymbol β vector of the input distribution via Lambert W MLE (In general this is not exactly identical to \widehat{\boldsymbol β}_{MLE} for the input data),

theta

list; MLE for θ,

type

see Arguments,

hessian

Hessian matrix; used to calculate standard errors (only if hessian = TRUE, otherwise NULL),

call

function call,

distname

see Arguments,

message

message from the optimization method. What kind of convergence?,

method

estimation method; here "MLE".

Examples


# See ?LambertW-package


LambertW documentation built on Sept. 22, 2022, 5:07 p.m.