An alternative multivariate skew Laplace distribution: properties and estimation

Arslan, Olçay

doi:10.1007/s00362-008-0183-7

Cited by 44 publications

(41 citation statements)

References 26 publications

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“…However, due to the special representation (7), one can implement the expectation-maximization (EM) algorithm while treating the unobservable random variance Z as a missing value and exploiting the fact that this random variable given the observed value Y has the generalized inverse Gaussian distribution. This method proved to efficiently produce the MLEs for some classes of distributions related to generalized Laplace ones; see [2,14,20]. The method can be adopted for a wide range of linear models involving the generalized multivariate Laplace laws.…”

Section: Maximum Likelihood and Em Algorithmmentioning

confidence: 98%

“…Since the sums such as (2) frequently appear in many applied problems in biology, economics, insurance mathematics, reliability, and other fields (see examples in [15] and references therein), AL distributions have a wide variety of applications; see [17]. The AL distributions play an analogous role among the heavy tailed geometric stable laws approximating sums (2) without the restriction of finite second moment (see [16]), as the Gaussian distributions do among the stable laws-they have finite moments of all orders, and their theory is elegant and straightforward.…”

Section: Introductionmentioning

confidence: 99%

“…The AL distributions play an analogous role among the heavy tailed geometric stable laws approximating sums (2) without the restriction of finite second moment (see [16]), as the Gaussian distributions do among the stable laws-they have finite moments of all orders, and their theory is elegant and straightforward. However, in spite of finiteness of moments, their tails are substantially longer than those of the Gaussian laws.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Multivariate generalized Laplace distribution and related random fields

Kozubowski

Podgórski

Rychlik

2013

Journal of Multivariate Analysis

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a b s t r a c tMultivariate Laplace distribution is an important stochastic model that accounts for asymmetry and heavier than Gaussian tails, while still ensuring the existence of the second moments. A Lévy process based on this multivariate infinitely divisible distribution is known as Laplace motion, and its marginal distributions are multivariate generalized Laplace laws. We review their basic properties and discuss a construction of a class of moving average vector processes driven by multivariate Laplace motion. These stochastic models extend to vector fields, which are multivariate both in the argument and the value. They provide an attractive alternative to those based on Gaussianity, in presence of asymmetry and heavy tails in empirical data. An example from engineering shows modeling potential of this construction.

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Section: Maximum Likelihood and Em Algorithmmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Multivariate generalized Laplace distribution and related random fields

Kozubowski

Podgórski

Rychlik

2013

Journal of Multivariate Analysis

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“…Recently, various members of this class, which is also known as a location-scale mixture distributions, have been considered and studied in the literature (see e.g. Arslan (2010Arslan ( , 2015, Nematollahi et al (2016)). As a special case of NMV distributions, Barndorff-Nielsen (1977) introduced the family of Generalized Hyperbolic (GH) distributions for modeling dune movements.…”

Section: Introductionmentioning

confidence: 99%

On the Finite Mixture Modelling via Normal Mean-variance Birnbaum-Saunders Distribution

Naderi¹,

Arabpour²,

Jamalizadeh³

2017

JIRSS

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Abstract. This paper presents a new finite mixture model using the normal meanvariance mixture of Birnbaum-Saunders distribution. The proposed model is multimodal with wider ranges of skewness and kurtosis. Moreover, it is useful for modeling highly asymmetric data in various theoretical and applied statistical problems. The maximum likelihood estimates of the parameters of the model are computed iteratively by feasible EM algorithm. To illustrate the finite sample properties and performance of the estimators, we conduct a simulation study and illustrate the usefulness of the new model by analyzing a real dataset.

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“…Lange and Sinsheimer (1993) defined a multivariate version of the laplace distribution as a scale mixture of the multivariate normal distribution which has longer tail than the multivariate normal distributions and hence may provide a useful alternative for modeling purposes. Multivariate laplace distribution was extended to multivariate skew-laplace distribution, using a normal variance-mean mixture model with a gamma mixture by Arslan (2010). Also Arslan and Genc (2009) studied skew generalized t (SGT) distribution as the scale mixture of a skew exponential power distribution by providing an iterative re-weighting algorithm to compute the maximum likelihood estimates for the parameters identified as an EM-type algorithm.…”

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confidence: 99%

Inference and further probabilistic properties of the $$ SUN_{n,2}$$ S U N n , 2 -distribution

2014

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In this paper the normal-skew-normal distribution, proposed by Gomez et al. (Statistics 47:411-421, 2013), is extended to the multivariate case. It is also a special case of SU N n,2 -distribution, recently studied by Arellano-Valle and Genton (Chil J Stat 2:17-34, 2010). We show that the proposed distribution can be expressed as a shape mixture of the multivariate extended skew-normal distribution. Applying this property leads to deriving stochastic representations for the proposed distribution. Also we give some basic properties for this new family. Computational techniques using EM-type algorithms are employed for iteratively computing maximum likelihood estimates. Finally, an application of the new distribution is illustrated using some real data sets.

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An alternative multivariate skew Laplace distribution: properties and estimation

Cited by 44 publications

References 26 publications

Multivariate generalized Laplace distribution and related random fields

Multivariate generalized Laplace distribution and related random fields

On the Finite Mixture Modelling via Normal Mean-variance Birnbaum-Saunders Distribution

Inference and further probabilistic properties of the $$ SUN_{n,2}$$ S U N n , 2 -distribution

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