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Zhenghong Wang 《统计学通讯:理论与方法》2018,47(13):3192-3203
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ABSTRACTRandom vectors with positive components are common in many applied fields, for example, in meteorology, when daily precipitation is measured through a region Marchenko and Genton (2010). Frequently, the log-normal multivariate distribution is used for modeling this type of data. This modeling approach is not appropriate for data with high asymmetry or kurtosis. Consequently, more flexible multivariate distributions than the log-normal multivariate are required. As an alternative to this distribution, we propose the log-alpha-power multivariate and log-skew-normal multivariate models. The first model is an extension for positive data of the fractional order statistics model Durrans (1992). The second one is an extension of the log-skew-normal model studied by Mateu-Figueras and Pawlowsky-Glahn (2007). We study parameter estimation for these models by means of pseudo-likelihood and maximum likelihood methods. We illustrate the proposal analyzing a real dataset. 相似文献
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We consider a new generalization of the skew-normal distribution introduced by Azzalini (1985). We denote this distribution Beta skew-normal (BSN) since it is a special case of the Beta generated distribution (Jones, 2004). Some properties of the BSN are studied. We pay attention to some generalizations of the skew-normal distribution (Bahrami et al., 2009; Sharafi and Behboodian, 2008; Yadegari et al., 2008) and to their relations with the BSN. 相似文献
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This paper addresses a generalization of the bivariate Cauchy distribution discussed by Fang et al. (1990), derived from a trivariate normal distribution with a general correlation matrix. We obtain explicit expressions for the joint distribution function and joint density function, and show that they reduce in a special case to the corresponding expressions of Fang et al. (1990). Finally, we show that this generalized distribution is useful in determining the orthant probability of a bivariate skew-normal distribution of Azzalini and Dalla Valle (1996). 相似文献
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《Journal of Statistical Computation and Simulation》2012,82(11):1679-1699
Item response theory (IRT) comprises a set of statistical models which are useful in many fields, especially when there is an interest in studying latent variables (or latent traits). Usually such latent traits are assumed to be random variables and a convenient distribution is assigned to them. A very common choice for such a distribution has been the standard normal. Recently, Azevedo et al. [Bayesian inference for a skew-normal IRT model under the centred parameterization, Comput. Stat. Data Anal. 55 (2011), pp. 353–365] proposed a skew-normal distribution under the centred parameterization (SNCP) as had been studied in [R.B. Arellano-Valle and A. Azzalini, The centred parametrization for the multivariate skew-normal distribution, J. Multivariate Anal. 99(7) (2008), pp. 1362–1382], to model the latent trait distribution. This approach allows one to represent any asymmetric behaviour concerning the latent trait distribution. Also, they developed a Metropolis–Hastings within the Gibbs sampling (MHWGS) algorithm based on the density of the SNCP. They showed that the algorithm recovers all parameters properly. Their results indicated that, in the presence of asymmetry, the proposed model and the estimation algorithm perform better than the usual model and estimation methods. Our main goal in this paper is to propose another type of MHWGS algorithm based on a stochastic representation (hierarchical structure) of the SNCP studied in [N. Henze, A probabilistic representation of the skew-normal distribution, Scand. J. Statist. 13 (1986), pp. 271–275]. Our algorithm has only one Metropolis–Hastings step, in opposition to the algorithm developed by Azevedo et al., which has two such steps. This not only makes the implementation easier but also reduces the number of proposal densities to be used, which can be a problem in the implementation of MHWGS algorithms, as can be seen in [R.J. Patz and B.W. Junker, A straightforward approach to Markov Chain Monte Carlo methods for item response models, J. Educ. Behav. Stat. 24(2) (1999), pp. 146–178; R.J. Patz and B.W. Junker, The applications and extensions of MCMC in IRT: Multiple item types, missing data, and rated responses, J. Educ. Behav. Stat. 24(4) (1999), pp. 342–366; A. Gelman, G.O. Roberts, and W.R. Gilks, Efficient Metropolis jumping rules, Bayesian Stat. 5 (1996), pp. 599–607]. Moreover, we consider a modified beta prior (which generalizes the one considered in [3]) and a Jeffreys prior for the asymmetry parameter. Furthermore, we study the sensitivity of such priors as well as the use of different kernel densities for this parameter. Finally, we assess the impact of the number of examinees, number of items and the asymmetry level on the parameter recovery. Results of the simulation study indicated that our approach performed equally as well as that in [3], in terms of parameter recovery, mainly using the Jeffreys prior. Also, they indicated that the asymmetry level has the highest impact on parameter recovery, even though it is relatively small. A real data analysis is considered jointly with the development of model fitting assessment tools. The results are compared with the ones obtained by Azevedo et al. The results indicate that using the hierarchical approach allows us to implement MCMC algorithms more easily, it facilitates diagnosis of the convergence and also it can be very useful to fit more complex skew IRT models. 相似文献
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Mohsen Pourahmadi 《统计学通讯:理论与方法》2013,42(9):1803-1819
Multivariate skew-normal (SN) distributions (Azzalini and Dalla Valle, 1996) enjoy some of the useful properties of normal distributions, have nonlinear heteroscedastic predictors but lack the closure property of normal distributions (the sum of independent SN random variables is not SN). Recently, there has been a proliferation of classes of SN distributions with certain closure properties, one of the most promising being the closed skew-normal (CSN) distributions of González-Farías et al. (2004). We study the construction of stationary SN ARMA models for colored SN noise and show that their finite-dimensional distributions are skew-normal, seldom strictly stationary and their covariance functions differ from their normal ARMA counterparts in that they do not converge to zero for large lags. The situation is better for ARMA models driven by CSN noise, but at the additional cost of considerable computational complexity and a less explicit skewness parameter. In view of these results, the widespread use of such classes of SN distributions in the framework of ARMA models seem doubtful. 相似文献
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