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The skew normal distribution family is an attractive distribution family due to its mathematical tractability and inclusion of the normal distribution as the special case. It has wide applications in many applied fields such as finance, economics, and medical research. Such a distribution family has been studied extensively since it was introduced by Azzalini in 1985 for the first time. Yet, few work has been done on the study of change point problem related to this distribution family. In this article, we propose the likelihood ratio test (LRT) to detect changes in the parameters of the skew normal distribution associated with some asymptotic results of the test statistic. Simulations have been conducted under different scenarios to investigate the performance of the proposed method. Comparisons to some other existing method indicate the comparable power of the method in detecting changes in parameters of the skew normal distribution model. Applications on two real data: Brazilian and Tanzanian stock returns illustrate the detection procedure. 相似文献
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Antonio Canale 《统计学通讯:理论与方法》2013,42(12):2507-2516
The construction of regions with assigned probability p and minimum geometric measure has theoretical and practical interests, such as the construction of tolerance regions. Following Azzalini (2001) and exploiting the normal approximation of the extended skew-normal distribution when some of its parameters go to infinity, we discuss an approach for the construction of regions with assigned probability p for the bivariate extended skew-normal distribution. 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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We consider the asymptotic distribution of divergence-based influence measures which are an extension for polytomous logistic regression of an influence measure proposed in Johnson (1985), for binary logistic regression. A numerical example compares the classical Cook’s distance with the divergence based influence measures. 相似文献
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Baker (2008) introduced a new class of bivariate distributions based on distributions of order statistics from two independent samples of size n. Lin and Huang (2010) discovered an important property of Baker’s distribution and showed that the Pearson’s correlation coefficient for this distribution converges to maximum attainable value, i.e., the correlation coefficient of the Fréchet upper bound, as n increases to infinity. Bairamov and Bayramoglu (2013) investigated a new class of bivariate distributions constructed by using Baker’s model and distributions of order statistics from dependent random variables, allowing higher correlation than that of Baker’s distribution. In this article, a new class of Baker’s type bivariate distributions with high correlation are constructed based on distributions of order statistics by using an arbitrary continuous copula instead of the product copula. 相似文献
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Two-period crossover design is one of the commonly used designs in clinical trials. But, the estimation of treatment effect is complicated by the possible presence of carryover effect. It is known that ignoring the carryover effect when it exists can lead to poor estimates of the treatment effect. The classical approach by Grizzle (1965) consists of two stages. First, a preliminary test is conducted on carryover effect. If the carryover effect is significant, analysis is based only on data from period one; otherwise, analysis is based on data from both periods. A Bayesian approach with improper priors was proposed by Grieve (1985) which uses a mixture of two models: a model with carryover effect and another without. The indeterminacy of the Bayes factor due to the arbitrary constant in the improper prior was addressed by assigning a minimally discriminatory value to the constant. In this article, we present an objective Bayesian estimation approach to the two-period crossover design which is also based on a mixture model, but using the commonly recommended Zellner–Siow g-prior. We provide simulation studies and a real data example and compare the numerical results with Grizzle (1965)’s and Grieve (1985)’s approaches. 相似文献
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AbstractThis article is devoted to study the problem of test of periodicity in the restricted exponential autoregressive (EXPAR) model. The local asymptotic normality property, of this model, is shown via the adapted sufficient conditions due to Swensen (1985). Using this result, in the case where the innovation density is specified, we obtain a parametric local asymptotic “most stringent” test. 相似文献
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A new class of lifetime distributions, which can exhibit with upside-down bathtub-shaped, bathtub-shaped, decreasing, and increasing failure rates, is introduced. The new distribution is constructed by compounding generalized Weibull and logarithmic distributions, leading to improvement on the lifetime distribution considered in Dimitrakopoulou et al. (2007) by having no restriction on the shape parameter and extending the result studied by Tahmasbi and Rezaei (2008) in the general form. The proposed model includes the exponential–logarithmic and Weibull–logarithmic distributions as special cases. Various statistical properties of the proposed class are discussed. Furthermore, estimation via the maximum likelihood method and the Fisher information matrix are discussed. Applications to real data demonstrate that the new class of distributions is more flexible than other recently proposed classes. 相似文献
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This article compares three value-at-risk (VaR) approximation methods suggested in the literature: Cornish and Fisher (1937), Sillitto (1969), and Liu (2010). Simulation results are obtained for three families of distributions: student-t, skewed-normal, and skewed-t. We recommend the Sillitto approximation as the best method to evaluate the VaR when the financial return has an unknown, skewed, and heavy-tailed distribution. 相似文献
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S. Shams Harandi 《统计学通讯:理论与方法》2013,42(8):2204-2227
AbstractIn this article, we introduce a new class of lifetime distributions. This new class includes several previously known distributions such as those of Chahkandi and Ganjali (2009), Mahmoudi and Jafari (2012), and Nadarajah et al. (2012). This new class of four-parameter distributions allows for flexible failure rate behavior. Indeed, the failure rate function here can be increasing, decreasing, bathtub-shaped or upside-down bathtub-shaped. Several distributional properties of the new class including moments, quantiles and order statistics are studied. An EM algorithm for computing the estimates of the parameters involved is proposed and some maximum entropy characterizations are discussed. Finally, to show the flexibility and potential of the new class of distributions, applications to two real data sets are provided. 相似文献
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Marcelo de Paula 《统计学通讯:理论与方法》2013,42(19):5762-5786
ABSTRACTIn this article, we propose an approach for incorporating continuous and discrete original outcome distributions into the usual exponential family regression models. The new approach is an extension of the works of Suissa (1991) and Suissa and Blais (1995), which present methods to estimate the risk of an event defined in a sample subspace of an original continuous outcome variable. Simulation studies are presented in order to illustrate the performance of the developed methodology. Real data sets are analyzed by using the proposed 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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Suchandan Kayal 《统计学通讯:理论与方法》2018,47(20):4938-4957
Several probability distributions such as power-Pareto distribution (see Gilchrist 2000 and Hankin and Lee 2006), various forms of lambda distributions (see Ramberg and Schmeiser 1974 and Freimer et al. 1988), Govindarajulu distribution (see Nair, Sankaran, and Vineshkumar 2012), etc., do not have manageable distribution functions, though they have tractable quantile functions. Hence, analytical study of the properties of Chernoff distance of two random variables associated with these distributions via traditional distribution function-based tool becomes difficult. To make this simple, in this paper, we introduce quantile-based Chernoff distance for (left or right) truncated random variables and study its various properties. Some useful bounds as well as characterization results are obtained. 相似文献
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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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In this article, we directly introduce the continuous version of the general discrete triangular distributions (Kokonendji and Zocchi, 2010). It is bounded and, in general, unimodal with pike. It contains thus a very useful class of two-sided power distributions (van Dorp and Kotz, 2002a,b, 2003). Moments, particular cases, limit distributions, and relations between parameters are straightforwardly derived. 相似文献
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Mike G. Tsionas 《统计学通讯:理论与方法》2018,47(12):3022-3028
The properties of high-dimensional Bingham distributions have been studied by Kume and Walker (2014). Fallaize and Kypraios (2016) propose the Bayesian inference for the Bingham distribution and they use developments in Bayesian computation for distributions with doubly intractable normalizing constants (Møller et al. 2006; Murray, Ghahramani, and MacKay 2006). However, they rely heavily on two Metropolis updates that they need to tune. In this article, we propose instead a model selection with the marginal likelihood. 相似文献
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Mahmoud Riad Mahmoud 《统计学通讯:理论与方法》2013,42(20):4396-4407
In this article, the exact form of Fisher information matrix for the generalized Feller-Pareto (GFP) distribution is determined. The GFP family is a general distribution which includes a variety of distributions as special cases. For example:??generalized Singh-Maddala distribution which in turn includes Burr, Fisk, and Lomax distribution (see Kleiber and Kotz, 2003);??a Pareto IV distribution which includes a hierarchy of Pareto models, omitted an additional location parameter (see Arnold, 1983, 2008); and??beta Lomax distribution which includes, for example, beta II and Lomax distributions.Application of these distributions covers a wide spectrum of areas ranging from actuarial science, economics, finance to bioscience, telecommunications, and medicine. 相似文献
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In this article, necessary conditions for comparing order statistics from distributions with regularly varying tails are discussed in terms of various stochastic orders. A necessary and sufficient condition for stochastically comparing tail behaviors of order statistics is derived. The main results generalize and recover some results in Kleiber (2002, 2004). Extensions to coherent systems are mentioned as well. 相似文献
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For the multivariate elliptical model subjective Bayesian estimators of the location vector and some functions of the characteristic matrix with the normal-inverse Wishart and the normal-Wishart as prior, respectively, are derived. Fang and Li (1999) considered the elliptical model for Bayesian analysis for an objective prior structure. In addition, the newly developed results are applied to the multivariate normal- and t-distribution. A performance study is done to evaluate the normal-gamma and normal-inverse gamma distributions as suitable priors. A practical application for the posterior distributions of the multivariate t-distribution is included by means of Gibbs sampling and a Metropolis-Hastings algorithm. 相似文献