Statistical inference for a general class of asymmetric distributions

Arellano–Valle, Reinaldo B.; Gómez, Héctor W.; Quintana, Fernando A.

doi:10.1016/j.jspi.2003.11.014

Cited by 129 publications

(103 citation statements)

References 9 publications

Supporting

Mentioning

102

Contrasting

Order By: Relevance

“…Of course, a(γ), b(γ) > 0 and when a(γ) = b(γ), a rescaled version of (1.2) returns. This particular way of parametrising the distribution is due to Arellano-Valle, Gómez & Quintana (2005) and will be discussed further below. Two-piece distributions have a long history.…”

Section: The Four-parameter Casementioning

confidence: 99%

“…In particular, the aesthetically pleasing choice a(γ) = 1/γ, b(γ) = γ (Fernández & Steel, 1998, Jones, 2006 is not an appropriate parametrisation in this sense. It should also be noted that the efficacy of this parametrisation is suggested by the information matrix in the special case of the two-piece exponential power distribution with fixed δ provided by Arellano-Valle et al (2005): it includes ι µσ = ι γσ = 0.…”

Section: Likelihood Fitting In the Arellano-valle Et Al Parametrisationmentioning

confidence: 99%

“…However, one specific model, a "two-piece" skew-t distribution (Fernández & Steel, 1998) with a particular parametrisation of skewness (Arellano-Valle, Gómez & Quintana, 2005) appears in the literature within which this is not the case: location and skewness parameter are tied up, as are scale and tailweight parameters, but each of the former pair are asymptotically independent of each of the latter. An information matrix of this form was first produced in this special case -but without further comment -by Gómez, Torres & Bolfarine (2007).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On parameter orthogonality in symmetric and skew models

Jones

Anaya-Izquierdo

2011

Journal of Statistical Planning and Inference

View full text Add to dashboard Cite

Orthogonal and partly orthogonal reparametrisations are provided for certain wide and important families of univariate continuous distributions. First, the orthogonality of parameters in location-scale symmetric families is extended to symmetric distributions involving a third parameter. This sets the scene for consideration of the four-parameter situation in which skewness is also allowed. It turns out that one specific approach to generating such fourparameter families, that of two-piece distributions with a certain parametrisation restriction, has some attractive features with regard to parameter orthogonality. This work also affords partly orthogonal parametrisations of three-parameter two-piece models.

show abstract

Section: The Four-parameter Casementioning

confidence: 99%

Section: Likelihood Fitting In the Arellano-valle Et Al Parametrisationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On parameter orthogonality in symmetric and skew models

Jones

Anaya-Izquierdo

2011

Journal of Statistical Planning and Inference

View full text Add to dashboard Cite

show abstract

“…Henze (1986) obtained a stochastic representation for the SN and used it to obtain its odd moments. A comprehensive treatment of the skew normal family of distributions can be found in Genton (2004), Arellano-Valle et al (2004, 2005 and Gupta et al (2002).…”

Section: Introductionmentioning

confidence: 99%

“…This class consists of truncated mixtures that are known as split distributions or two-piece distributions. This family is presented by Fernandez and Steel (1998) and generalized by Arellano-Valle et al (2005). 1 Its generalized form is…”

Section: Introductionmentioning

confidence: 99%

The Continuous Hidden Threshold Mixed Skew-Symmetric Distribution

Bouaddi

Belhachemi²,

Douch³

2015

SSRN Journal

View full text Add to dashboard Cite

This paper explores a way to construct a new family of univariate probability distributions where the parameters of the distribution capture the dependence between the variable of interest and the continuous latent state variable (the regime). The distribution nests two well known families of distributions, namely, the skew normal family of Azzalini (1985) and a mixture of two Arnold et al. (1993) distribution. We provide a stochastic representation of the distribution which enables the user to easily simulate the data from the underlying distribution using generated uniform and normal variates. We also derive the moment generating function and the moments. The distribution comprises eight free parameters that make it very flexible. This flexibility allows the user to capture many stylized facts about the data such as the regime dependence, the asymmetry and fat tails as well as thin tails.

show abstract