Multivariate log‐skew‐elliptical distributions with applications to precipitation data

Marchenko, Yulia; Genton, Marc G.

doi:10.1002/env.1004

Cited by 60 publications

(56 citation statements)

References 27 publications

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“…We use the notation Y ∼ LSN ( ξ , η , λ ). Real data applications of this model can be found in Azzalini et al (, in Marchenko and Genton () in a multivariate setting and in Bolfarine et al () in a bimodal context. Notice that if λ = 0, then the ordinary LN distribution follows.…”

Section: Introductionmentioning

confidence: 99%

The log‐power‐normal distribution with application to air pollution

2014

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In this article, we study an extension of the power-normal distribution to the case of the more flexible log-power-normal distribution. We find the density function and study some properties of the new distribution, deriving a general expression for its moments. Parameter estimation is implemented by using the moments and the maximum likelihood approaches. We obtain the Fisher information matrix for the new model, which is shown to be nonsingular in the vicinity of symmetry. Results of an application to air contamination data indicate good performance of the proposed model, validating a modification of Ahrens' law.

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Section: Introductionmentioning

confidence: 99%

The log‐power‐normal distribution with application to air pollution

2014

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“…The distribution of non-zero rain rates is nonGaussian with a heavy tail at high rain rates. A number of different distributions have been used to represent the conditional rain rate (the rain rate when raining), such as the lognormal or gamma distributions (Essenwanger 1985) and logskew-elliptical distributions (Marchenko and Genton 2010). The rain model and the resulting form of the space-time covariance function are described in more detail in Sect.…”

Section: Introductionmentioning

confidence: 99%

A Matérn model of the spatial covariance structure of point rain rates

Sun

Bowman

Genton

et al. 2014

Stoch Environ Res Risk Assess

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It is challenging to model a precipitation field due to its intermittent and highly scale-dependent nature. Many models of point rain rates or areal rainfall observations have been proposed and studied for different time scales. Among them, the spectral model based on a stochastic dynamical equation for the instantaneous point rain rate field is attractive, since it naturally leads to a consistent space-time model. In this paper, we note that the spatial covariance structure of the spectral model is equivalent to the well-known Matérn covariance model. Using highquality rain gauge data, we estimate the parameters of the Matérn model for different time scales and demonstrate that the Matérn model is superior to an exponential model, particularly at short time scales.

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“…Hence, a lognormal model is often adopted for nonzero pre-cipitation measurements, see Lee and Zawadzki (2005) and Fuentes et al (2008). Alternative approaches also exist in the literature such as the truncated power transformation of Bardossy and Plate (1992) and the use of skew-elliptical distributions in Marchenko and Genton (2010). Our approach is motivated by Fuentes et al (2008), where a zero-inflated log-Gaussian model has been used for rainfall, and, in a hierarchical framework, the distribution of no rainfall events was modeled to depend on the true rainfall intensity.…”

Section: Introductionmentioning

confidence: 99%

An adaptive spatial model for precipitation data from multiple satellites over large regions

Chakraborty

De²,

Bowman

et al. 2013

Stat Comput

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Satellite measurements have of late become an important source of information for climate features such as precipitation due to their near-global coverage. In this article, we look at a precipitation dataset during a 3-hour window over tropical South America that has information from two satellites. We develop a flexible hierarchical model to combine instantaneous rainrate measurements from those satellites while accounting for their potential heterogeneity. Conceptually, we envision an underlying precipitation surface that influences the observed rain as well as absence of it. The surface is specified using a mean function centered at a set of knot locations, to capture the local patterns in the rainrate, combined with a residual Gaussian process to account for global correlation across sites. To improve over the commonly used pre-fixed knot choices, an efficient reversible jump scheme is used to allow the number of such knots as well as the order and support of associated polynomial terms to be chosen adaptively.To facilitate computation over a large region, a reduced rank approximation for the parent Gaussian process is employed.

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Multivariate log‐skew‐elliptical distributions with applications to precipitation data

Cited by 60 publications

References 27 publications

The log‐power‐normal distribution with application to air pollution

The log‐power‐normal distribution with application to air pollution

A Matérn model of the spatial covariance structure of point rain rates

An adaptive spatial model for precipitation data from multiple satellites over large regions

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