Estimate the Four Parameters of Stable Laws using Different Methods

Estimate the four parameters of stable laws using maximum likelihood method, generalised method of moments with finite and continuum number of points, iterative Koutrouvelis regression and Kogon-McCulloch method. The asymptotic properties of the estimators (covariance matrix, confidence intervals) are also provided.

Installing StableEstim

The latest stable version is on CRAN.

install.packages("StableEstim")

You can install the development version of StableEstim from Github:

remotes::install_github("GeoBosh/StableEstim")

Overview

A collection of methods to estimate the four parameters of stable distributions. The package also provides functions to compute characteristic functions and tools to run Monte Carlo simulations.

The main functions of package StableEstim are briefly described below:

• main function: Estim() estimates the parameters by various methods. Also gives the associated asymptotic properties of the estimators.

• estimation functions for specific methods: these functions are called by Estim() but can be used directly, as well. The methods provided so far are:

  • the maximum-likelihood (MLParametersEstim()),

  • the generalised method of moments with a finite (GMMParametersEstim()) or continuum moment conditions (CgmmParametersEstim()),

  • the iterative Koutrouvelis regression method (KoutParametersEstim()),

  • the fast Kogon-McCulloch method used for first guess estimation (IGParametersEstim).

• characteristic function: the characteristic function (ComplexCF()) and its Jacobian (jacobianComplexCF()) can be computed and will return a vector (respectively a matrix) of complex numbers.

• Monte Carlo simulation: a tool to run a Monte Carlo simulation (Estim_Simulation()) is provided and can save output files and/or produce statistical summary.

The package is developed by Tarak Kharrat and Georgi N.Boshnakov.