股票投资组合的实证研究

股票的收益率的实际分布有尖峰厚尾有偏的特性,而传统的正态分布不能很好地拟合这一特性。对股票进行组合投资是现代投资的趋势。本文基于非对称Laplace分布来研究股票投资组合。实证分析表明,非对称Laplace分布比正态分布,对称Laplace分布能更好地拟合组合资产的收益分布率。     

斜t及斜Laplace分布

本文首先介绍一种用来处理重尾数据的斜t分布,并给出其相应的基本数字特征.基于Laplace分布的对称性及重尾性,定义一种新的分布一斜Laplace分布,推导出新分布的密度函数和分布函数,且通过密度函数曲线图书其与Laplace分布进行比较.最后,证实所提斜Laplace分布的重尾性质.     

有限混合Laplace分布回归模型局部估计的EM算法

本文研究了一类有限混合Laplace分布回归模型的局部极大似然估计问题. 利用核回归方法和最大化局部加权似然函数的EM算法, 获得了参数函数的局部极大似然估计量, 并讨论了它们的渐近偏差, 渐近方差和渐近正态性. 推广了有限混合回归模型下局部非参数估计的结果.     

Marshall-Olkin扩展重尾分布的刻画

利用Marshall-Olkin提出构造分布的方法,以重尾分布F作为基础,提出了Marshall-Olkin扩展重尾分布G,根据常见重尾分布子族的定义及其等价关系,分析了F与G的相关性质,对于重尾分布族,G具有封闭性,尾等价性,同时在连续型分布情形下,讨论了F与G的密度函数之间及风险率函数之间的关系.最后,将Marshall-Olkin扩展重尾分布应用于实际数据中,并在拟合数据方面与原分布进行比较,表明扩展分布要优于原分布.     

股票期权VaR的一种计算方法

本文提出一种运用Laplace分布来计算股票期权VaR的新方法.首先对股票价格的运动规律进行理论和实证分析,表明利用Laplace分布来来拟合股票的对数收益率是合理的,然后在此基础上推导了股票期权VaR的计算公式,最后给出了算例.     

关于Laplace分布的一个强极限定理

利用似然比构造几乎处处收敛的上鞅 ,结合分析方法 ,给出了 Laplace分布的一个强极限定理 .     

深沪股市收益率分布特征的统计分析

本文通过对深沪两地股票市场的股指收益率数据进行分析,发现两地股票收益率分布均呈现"尖峰厚尾"反正态特征,本文通过引入Laplace分布代替过去人们常用的正态分布去刻画收益率分布,结果显示Laplace分布比正态分布拟合效率有了明显的提高。     

Yamabe流上Laplace算子特征值的一个单调性应用

讨论了紧致无边流形上Laplace算子的特征值在Yamabe流上随时间的变化情况,结合极值原理得到了Laplace算子特征值的单调性.     

有向图的Laplace谱半径

Laplace矩阵的谱半径一直是近年来谱图理论的研究热点.本文主要讨论有向图Laplace矩阵的谱半径,用顶点的出度和公共邻域数给出了谱半径上界,用图的最大出度给出了一些特殊图类谱半径的下界.     

具有相关索赔风险模型的破产概率

本文考虑了具有两类索赔的风险模型,这两类索赔的计数过程是相关的Poisson过程和Erlang过程.通过Laplace变换方法,得到了该风险模型在索赔额为任意分布情形下破产概率的计算公式,并在索赔额为指数分布的情形下,得到了破产概率的精确表达式.     

On the logistic midrange

Summary It is well-known that for a large family of distributions, the sample midrange is asymptotically logistic. In this article, the logistic midrange is closely examined. Its distribution function is derived using Dixon's formula (Bailey (1935,Generalized Hypergeometric Series, Cambridge University Press, p. 13)) for the generalized hypergeometric function with unit argument, together with appropriate techniques for the inversion of (bilateral) Laplace transforms. Several relationships in distribution are established between the midrange and sample median of the logistic and Laplace random variables. Possible applications in testing for outliers are also discussed.     

Correction to “On the linear combination of normal and Laplace random variables”, by Nadarajah,S., <Emphasis Type="Italic">Computational Statistics</Emphasis>, 2006, <Emphasis Type="Bold">21</Emphasis>, 63–71

In the above mentioned paper, some errors were found in the expressions given for the distribution of a linear combination of Normal and Laplace random variables, Z, given in formulae (3, Theorem 1), (6), and (7) that can lead to obtaining negative values for the mentioned distribution. The corrected versions for these expressions are presented here. In addition, the density function of Z is also provided.     

A Skew Laplace Distribution on Integers

We propose a discrete version of the skew Laplace distribution. In contrast with the discrete normal distribution, here closed form expressions are available for the probability density function, the distribution function, the characteristic function, the mean, and the variance. We show that this distribution on integers shares many properties of the skew Laplace distribution on the real line, including unimodality, infinite divisibility, closure properties with respect to geometric compounding, and a maximum entropy property. We also discuss statistical issues of estimation under this model.     

The beta Laplace distribution

The Laplace distribution is one of the earliest distributions in probability theory. For the first time, based on this distribution, we propose the so-called beta Laplace distribution, which extends the Laplace distribution. Various structural properties of the new distribution are derived, including expansions for its moments, moment generating function, moments of the order statistics, and so forth. We discuss maximum likelihood estimation of the model parameters and derive the observed information matrix. The usefulness of the new model is illustrated by means of a real data set.     

Maximum Likelihood Estimation of Asymmetric Laplace Parameters

Maximum likelihood estimators (MLE's) are presented for the parameters of a univariate asymmetric Laplace distribution for all possible situations related to known or unknown parameters. These estimators admit explicit form in all but two cases. In these exceptions effective algorithms for computing the estimators are provided. Asymptotic distributions of the estimators are given. The asymptotic normality and consistency of the MLE's for the scale and location parameters are derived directly via representations of the relevant random variables rather than from general sufficient conditions for asymptotic normality of the MLE's.     

Tests of fit for the Rayleigh distribution based on the empirical Laplace transform

In this paper a class of goodness-of-fit tests for the Rayleigh distribution is proposed. The tests are based on a weighted integral involving the empirical Laplace transform. The consistency of the tests as well as their asymptotic distribution under the null hypothesis are investigated. As the decay of the weight function tends to infinity the test statistics approach limit values. In a particular case the resulting limit statistic is related to the first nonzero component of Neyman’s smooth test for this distribution. The new tests are compared with other omnibus tests for the Rayleigh distribution.     

The distribution of the zeros of L-functions and the least prime in some arithmetic progression

This paper gives some new estimations to the distribution of the zeros of L-functions and proves that the least prime in an arithmetic progression with a prime differenceq is ≪q ^4.5.