广义双曲线分布在概化理论偏态数据方差分量估计中的应用

心理与教育测量的应用领域发生了较大变化,被测群体的知识和能力等特质在一定程度上不再服从偏度为0的分布.文章利用广义双曲线分布性质,模拟生成一定偏度的偏态分布数据,探讨数据不同偏度对概化理论方差分量估计的影响.结果表明:利用广义双曲线分布性质可以有效模拟生成概化理论所需要的偏态分布数据；广义双曲线分布模拟的偏态分布数据对概化理论各种方法估计方差分量有影响.     

基于APARCH-Laplace模型的VaR和CVaR方法

针对我国证券市场收益率分布所表现出来的尖峰厚尾性,文章采Laplace分布刻画收益率分布,建立一种新的风险度量模型:APARCH-Laplace,并用实证分析证明了Laplace分布与正态分布相比,拟合数据较好。模型准确性检验表明用Laplace分布刻画收益率分布所计算的风险度量更有效。     

BOXPLOT—描述统计的一个简便工具

箱线图是描述统计的一个简便工具,其功能主要是识别数据批中的异常值;判断数据分布的偏态和尾重;比较不同数据批分布形状特征等。本文阐述了它的绘制、功能和应用。     

基于非对称Laplace分布研究VaR

风险价值(Value-at-Risk简称VaR)是度量市场风险的一种普遍使用的工具,可看作是市场风险度量的基石。本文基于非对称Laplace分布来研究VaR,详细地讨论了非对称Laplace分布的性质、参数估计,并用该分布去拟合中国股票市场收益率的分布。实证分析表明,非对称Laplace分布比正态分布、对称Laplace分布的拟合效果有明显的提高。     

Alpha正态分布及其在环境污染中的应用

目前,对实际数据的处理常采用一些对称分布,如正态分布和t分布等,而这种对称分布所给出的结果往往并不能令人满意。偏分布常用来处理有偏重尾数据,基于传统正态分布,提出一种处理偏态和重尾数据的alpha正态分布,并研究其参数估计方法及基本性质。将所提分布应用于环境污染数据,通过拟合检验alpha正态分布给出了很好的结果。     

基于g-h分布的极值分布拟合新方法

g-h分布是一种能对具有尖峰、厚尾、偏态特征的分布进行很好拟合的分布,还没有人将其专门用于分布尾部的局部拟合;同时g-h分布传统拟合方法是用分位数分别对其参数进行拟合的,这很难做到使四阶矩同时与目标分布一致。文章首先提出了g-h分布的蒙特卡罗算法;然后利用它进行股票收益率的极端值进行拟合;最后和极值分布拟合方法进行了对比分析。实证表明,g-h分布的蒙特卡罗算法比极值理论更加方便、灵活和准确。     

基于极值理论的组合分布模型

文章根据极值理论的性质构造了一种新的描述金融数据整体分布的组合分布。具体地说,尾部分布选取广义Pareto分布,中间分布选取偏t分布。文章还利用上证综合指数的历史数据对模型进行了检验,得到了令人满意的结果。     

基于GHSKT分布的WTI原油市场VaR风险度量

众所周知,同正态分布相比而言,金融市场的收益率变量具有偏态和尖峰厚尾特征。文章提出采用GHSKT分布来拟合收益率序列。为了解决参数估计难的问题,提出的强有力EM算法对于解决像包含Bessel函数这样复杂、具有大量局部最优解的优化问题,具有很现实的意义。最后,我们讨论GHSKT分布在WTI原油市场VaR风险度量中的应用。     

偏尾Laplace分布下的条件风险价值探讨

条件风险价值(CVaR)是学界目前广泛关注的一致性风险度量方法。文章在偏尾Laplace分布下研究了CVaR的估计问题,给出了CVaR的MLE估计,同时也讨论了CVaR估计的渐进性质和有限样本性质,并给出了CVaR估计的渐进分布和有限样本逼近方法,这对非对称厚尾分布下的金融风险管理具有一定的实用价值。此外,文章对如何评价CVaR估计也有一定的启发意义。     

中国股指收益率的非对称拉普拉斯分布实证检验

应用非对称拉普拉斯分布拟合沪深两市股指日、周收益率数据。研究结果表明:非对称拉普拉斯分布能够比正态分布更好地反映两市股指的日、周收益率数据的尖峰、厚尾、偏态特征。由于非对称拉普拉斯分布有显性的表达式,便于开展参数估计和数字特征的计算,因此对于股指期货投资者而言,在计算股指收益率的VaR、CVaR进行风险测量时,采用非对称拉普拉斯分布将是较好的选择。     

A new heavy-tailed distribution defined on the bounded interval: the logit slash distribution and its application

This paper proposes a new heavy-tailed and alternative slash type distribution on a bounded interval via a relation of a slash random variable with respect to the standard logistic function to model the real data set with skewed and high kurtosis which includes the outlier observation. Some basic statistical properties of the newly defined distribution are studied. We derive the maximum likelihood, least-square, and weighted least-square estimations of its parameters. We assess the performance of the estimators of these estimation methods by the simulation study. Moreover, an application to real data demonstrates that the proposed distribution can provide a better fit than well-known bounded distributions in the literature when the skewed data set with high kurtosis contains the outlier observations.     

A Generalization of the Univariate Slash by a Scale-Mixtured Exponential Power Distribution

A generalization of the slash distribution is derived using the scale mixture of the exponential power distribution. The newly defined family of distributions provides a rich flexibility on the tail heaviness and yields alternative robust estimators of location and scale in non normal situations. In order to investigate asymptotically the bias properties of the estimators, a simulation study is performed. The performance of the estimators on two well-known real data sets is also illustrated.     

Generalized modified slash distribution with applications

Abstract

In this article a generalization of the modified slash distribution is introduced. This model is based on the quotient of two independent random variables, whose distributions are a normal and a one-parameter gamma, respectively. The resulting distribution is a new model whose kurtosis is greater than other slash distributions. The probability density function, its properties, moments, and kurtosis coefficient are obtained. Inference based on moment and maximum likelihood methods is carried out. The multivariate version is also introduced. Two real data sets are considered in which it is shown that the new model fits better to symmetric data with heavy tails than other slash extensions previously introduced in literature.     

Modified slash distribution

In this paper we introduce a modified slash distribution obtained by modifying the usual slash distribution. This new distribution is based on the quotient of two independent random variables, whose distributions are the normal and the power of an exponential distribution of scale parameter equals to two, respectively. In this way, the result is a new distribution whose kurtosis values are greater when compared with that of the slash distribution. We study the density, some properties, moments, kurtosis and make inferences by the method of moments and maximum likelihood. We introduce a multivariate version of this new distribution. Moreover, we provide two illustrations with real data showing that the new distribution fits better the data than the ordinary slash distribution.     

A New Discrete Distribution Related to Generalized Gamma Distribution and Its Properties

In this article, a new discrete distribution related to the generalized gamma distribution (Stacy, 1962) is derived from a statistical mechanical setup. This new distribution can be seen as generalization of two-parameter discrete gamma distribution (Chakraborty and Chakravarty, 2012) and encompasses discrete version of many important continuous distributions. Some basic distributional and reliability properties, parameter estimation by different methods, and their comparative performances using simulation are investigated. Two-real life data sets are considered for data modeling and likelihood ratio test for illustrating the advantages of the proposed distribution over two-parameter discrete gamma distribution.     

A new family of multivariate slash distributions

In this article, a new form of multivariate slash distribution is introduced and some statistical properties are derived. In order to illustrate the advantage of this distribution over the existing generalized multivariate slash distribution in the literature, it is applied to a real data set.     

Bayesian analysis of generalized elliptical semi-parametric models

In this paper, we study the statistical inference based on the Bayesian approach for regression models with the assumption that independent additive errors follow normal, Student-t, slash, contaminated normal, Laplace or symmetric hyperbolic distribution, where both location and dispersion parameters of the response variable distribution include nonparametric additive components approximated by B-splines. This class of models provides a rich set of symmetric distributions for the model error. Some of these distributions have heavier or lighter tails than the normal as well as different levels of kurtosis. In order to draw samples of the posterior distribution of the interest parameters, we propose an efficient Markov Chain Monte Carlo (MCMC) algorithm, which combines Gibbs sampler and Metropolis–Hastings algorithms. The performance of the proposed MCMC algorithm is assessed through simulation experiments. We apply the proposed methodology to a real data set. The proposed methodology is implemented in the R package BayesGESM using the function gesm().     

A generalization of the multivariate slash distribution

In this paper, we propose a generalization of the multivariate slash distribution and investigate some of its properties. We show that the new distribution belongs to the elliptically contoured distributions family, and can have heavier tails than the multivariate slash distribution. Therefore, this generalization of the multivariate slash distribution can be considered as an alternative heavy-tailed distribution for modeling data sets in a variety of settings. We apply the generalized multivariate slash distribution to two real data sets to provide some illustrative examples.     

A generalized skew slash distribution via gamma-normal distribution

In this article, we introduce a generalization of the slash distribution via the gamma-normal distribution. We define the new slash distribution by relation of a gamma-normal random variable with respect to a power of a uniform random variable. The newly defined distribution generalizes the slash distribution and is more flexible in terms of its kurtosis and skewness than the slash distribution. Basic properties of the new distribution are studied. We derive the maximum likelihood estimators of its parameters and apply the distribution to a real dataset.     

Pareto Poisson–Lindley distribution with applications

A new lifetime distribution is introduced based on compounding Pareto and Poisson–Lindley distributions. Several statistical properties of the distribution are established, including behavior of the probability density function and the failure rate function, heavy- and long-right tailedness, moments, the Laplace transform, quantiles, order statistics, moments of residual lifetime, conditional moments, conditional moment generating function, stress–strength parameter, Rényi entropy and Song's measure. We get maximum-likelihood estimators of the distribution parameters and investigate the asymptotic distribution of the estimators via Fisher's information matrix. Applications of the distribution using three real data sets are presented and it is shown that the distribution fits better than other related distributions in practical uses.