fitBayes: Estimating parameters of the symmetric alpha-stable (SalphaS)...

In mixSSG: Clustering Using Mixtures of Sub Gaussian Stable Distributions

Estimating parameters of the symmetric α-stable (SαS) distribution using Bayesian paradigm.

Description

Let {{y}}_1,{{y}}_2, \cdots,{{y}}_n are n realizations form SαS distribution with parameters α, σ, and μ. Herein, we estimate parameters of symmetric univariate stable distribution within a Bayesian framework. We consider a uniform distribution for prior of tail thickness, that is α \sim U(0,2). The normal and inverse gamma conjugate priors are designated for μ and σ^2 with density functions given, respectively, by

π(μ)=\frac{1}{√{2π}σ_{0}}\exp\Bigl\{-\frac{1}{2}\Bigl(\frac{μ-μ_0}{σ_0}\Bigr)^{2}\Bigr\},

and

π(δ)= δ_{0}^{γ_{0}}δ^{-γ_0-1}\exp\Bigl\{-\frac{δ_0}{δ}\Bigr\},

where μ_0 \in R, σ_0>0, δ=σ^2, δ_0>0, and γ_0>0.

Usage

fitBayes(y, mu0, sigma0, gamma0, delta0, epsilon)

Arguments

y	vector of realizations that following SαS distribution.
mu0	the location hyperparameter corresponding to π(μ).
sigma0	the standard deviation hyperparameter corresponding to π(μ).
gamma0	the shape hyperparameter corresponding to π(δ).
delta0	the rate hyperparameter corresponding to π(δ).
epsilon	a positive small constant playing the role of threshold for stopping sampler.

Value

Estimated tail thickness, location, and scale parameters, number of iterations to attain convergence, the log-likelihood value across iterations, the Bayesian information criterion (BIC), and the Akaike information criterion (AIC).

Author(s)

Mahdi Teimouri

Examples

n <- 100
alpha <- 1.4
mu <- 0
sigma <- 1
y <- rnorm(n)
fitBayes(y, mu0 = 0, sigma0 = 0.2, gamma0 = 10e-5, delta0 = 10e-5, epsilon = 0.005)

mixSSG documentation built on Sept. 11, 2022, 5:06 p.m.