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1.
上证股指极值模型估计和VaR计算 总被引:2,自引:0,他引:2
桂文林 《数学的实践与认识》2008,38(19)
POT极值模型参数的准确估计是计算金融资产回报厚尾分布市场风险的关键.由n阶概率加权矩得到参数的二项式回归估计,而将参数的零,一阶概率加权矩估计予以推广.极大似然估计中.将极大化似然函转化为二元函数无条件极值问题·其他参数估计方法的结果作为迭代的初始值,通过它们的似然函数值和极大似然函数值的比较以及迭代次数判断方法的优劣.实证研究表明:参数的零、一阶概率加权矩估计较接近于真值,随着阶数的提高,二项式回归参数估计的误差很大.参数的极大似然估计优于非线性回归估计优于零、一阶概率加权矩估计.在此基础上计算上证A股指数vaR值. 相似文献
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指数分布冷贮备系统产品的统计分析——转换开关指数型的情形 总被引:1,自引:0,他引:1
给出了全样本场合下指数分布冷贮备系统产品寿命分布中参数θ≠λ时的矩估计和极大似然估计,通过Monte-Carlo给出了参数矩估计的精度,考察了1000次满足条件时所需要的模拟次数,随着样本量的增大,矩估计存在的比率逐渐增大,而极大似然估计的结果与样本有关.同时给出了参数θ=λ时的矩估计、极大似然估计和逆矩估计,通过Monte-Carlo模拟考察了参数点估计精度,认为矩估计比较优.文章还给出了求参数区间估计的两种方法——精确方法和近似方法,通过Monte-Carlo模拟认为精确方法精度较高. 相似文献
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广义Logistic分布族在生物、医学、金融管理,以及气象、水文、地质等领域有重要的应用。迄今为止,对此分布族的研究已取得了一系列重要成果;令人遗憾的是,关于三参数I型广义Logistic分布的研究还很不深入。本文利用矩法首先讨论三参数I型广义Logistic分布形状参数的估计,然后利用线性回归分析方法讨论分布的位置参数和刻度参数的估计,改进矩估计。本文所给出的分布参数的估计方法简单、有效;证明了在一定的条件下,本文给出的估计量存在、唯一,且模拟显示:估计量在中小样本情形下,一致优于分布参数的矩估计和L矩估计;特别是在样本容量n介于20和30之间时,估计量有更小的估计偏差和方差。估计方法简单、实用且有效。 相似文献
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广义Pareto分布的广义有偏概率加权矩估计方法 总被引:1,自引:0,他引:1
广义Pareto分布(GPD)是统计分析中一个极为重要的分布,被广泛应用于金融、保险、水文及气象等领域.传统的参数估计方法如极大似然估计、矩估计及概率加权矩估计方法等已被广泛应用,但使用中存在一定的局限性.虽然提出很多改进方法如广义概率加权矩估计、L矩和LH矩法等,但都是研究完全样本的估计问题,而在水文及气象等应用领域常出现截尾样本.本文基于概率加权矩理论,利用截尾样本对三参数GPD提出一种应用范围广且简单易行的参数估计方法,可有效减弱异常值的影响.首先求解出具有较高精度的形状参数的参数估计,其次得出位置参数及尺度参数的参数估计.通过Monte Carlo模拟说明该方法估计精度较高. 相似文献
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研究了P^-混合样本线性模型中的M估计,在较弱的矩条件下,获得了M估计是强相舍估计的充分条件.与相应结论比较,有了较大的实质性改进。 相似文献
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研究了混合样本线性模型中的M估计,在较弱的矩条件下,获得了M估计是强相合估计的充分条件.与相应结论比较,有了较大的实质性改进. 相似文献
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Kazuki Aoyama Kunio Shimizu S. H. Ong 《Annals of the Institute of Statistical Mathematics》2008,60(1):1-20
In this paper a univariate discrete distribution, denoted by GIT, is proposed as a generalization of the shifted inverse trinomial
distribution, and is formulated as a first-passage time distribution of a modified random walk on the half-plane with five
transition probabilities. In contrast, the inverse trinomial arises as a random walk on the real line with three transition
probabilities. The probability mass function (pmf) is expressible in terms of the Gauss hypergeometric function and this offers
computational advantage due to its recurrence formula. The descending factorial moment is also obtained. The GIT contains
twenty-two possible distributions in total. Special cases include the binomial, negative binomial, shifted negative binomial,
shifted inverse binomial or, equivalently, lost-games, and shifted inverse trinomial distributions. A subclass GIT3,1 is a particular member of Kemp’s class of convolution of pseudo-binomial variables and its properties such as reproductivity,
formulation, pmf, moments, index of dispersion, and approximations are studied in detail. Compound or generalized (stopped
sum) distributions provide inflated models. The inflated GIT3,1 extends Minkova’s inflated-parameter binomial and negative binomial. A bivariate model which has the GIT as a marginal distribution
is also proposed. 相似文献
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二项分布的参数估计问题研究 总被引:3,自引:0,他引:3
本文主要讨论二项分布的参数估计问题.对GB/T 4087.1-1983,GB/T 4087.2-1983,GB/T4087.3-1985给出的经典二项分布参数点估计、区间估计和可靠度置信下限计算方法进行了分析,指出了其中存在的问题.根据二项分布的数学表达式推导出了二项分布参数的概率分布密度函数,在此基础上提出了进行二项分布参数估计的一般方法. 相似文献
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Sharp bounds in terms of the first few binomial moments are found for the probability of a union of events, when the random variable denoting the number of events that occur follows symmetric distribution. Connection between the bounds of this paper and the bounds from a special case of the binomial moment problem of Prekopa (1995) is shown. As a special case, bounds for the probability when the underlying probability distribution is unimodal-symmetric are also found. 相似文献
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对二项分布的可靠度,提出了一种新的参数估计方法——E-Bayes估计法.在不同先验分布下,给出可靠度的E-Bayes估计和多层Bayes估计,并给出可靠度的E-Bayes估计的性质——E-Bayes估计和多层Bayes估计的关系.最后,给出了模拟算例,结果表明本文提出的方法可行且便于应用. 相似文献
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对目前普遍使用的期权定价二叉树模型的缺陷进行了分析,利用矩法构造出新型的二叉树参数模型.新的模型避免了负的概率并且具有很高的计算精度,因而可应用于计算各种期权的价格. 相似文献
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We consider a compound Poisson distribution generalized by a binomial distribution. Explicit representations are derived for the moment characteristics (ordinary and factorial cumulants, initial, factorial, binomial, and central moments) and various relationships and recurrences are proved. 相似文献
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For the compound Poisson law generalized by the negative binomial distribution we derive the explicit representation of the
probability function, the finite-difference recurrence, and expressions for the derivatives with respect to all parameters.
Explicit representations of ordinary and factorial cumulants to sixth order are given and asymptotic normality of the distribution
is proved. The distribution functions are constructed and analyzed for the most typical parameter values. Used to solve direct
and inverse problems by moment methods.
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Translated from Prikladnaya Matematika i Informatika, No. 19, pp. 91–102, 2004. 相似文献
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A. Kyriakoussis H. Papageorgiou 《Annals of the Institute of Statistical Mathematics》1989,41(4):671-676
The conditional distribution of Y given X=x, where X and Y are non-negative integer-valued random variables, is characterized in terms of the regression function of X on Y and the marginal distribution of X which is assumed to be of a power series form. Characterizations are given for a binomial conditional distribution when X follows a Poisson, binomial or negative binomial, for a hypergeometric conditional distribution when X is binomial and for a negative hypergeometric conditional distribution when X follows a negative binomial. 相似文献
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Choung Min Ng 《Applied mathematics and computation》2010,217(7):3069-3087
In this paper, we consider a new class of bivariate negative binomial distributions having marginal distributions with different index parameters. This feature is useful in statistical modelling and simulation studies, where different marginal distributions and a specified correlation are required. This feature also makes it more flexible than the existing bivariate generalizations of the negative binomial distribution, which have a common index parameter in the marginal distributions. Various interesting properties, such as canonical expansions and quadrant dependence, are obtained. Potential application of the proposed class of bivariate negative binomial distributions, as a bivariate mixed Poisson distribution, and computer generation of samples are examined. Numerical examples as well as goodness-of-fit to simulated and real data are also given here in order to illustrate the application of this family of bivariate negative binomial distributions. 相似文献
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We improve bounds of accuracy of the normal approximation to the distribution of a sum of independent random variables under relaxed moment conditions, in particular, under the absence of moments of orders higher than the second. We extend these results to Poisson binomial, binomial, and Poisson random sums. Under the same conditions, we obtain bounds for the accuracy of approximation of the distributions of mixed Poisson random sums by the corresponding limit law. In particular, we construct these bounds for the accuracy of approximation of the distributions of geometric, negative binomial, and Poisson-inverse gamma (Sichel) random sums by the Laplace, variance gamma, and Student distributions, respectively. 相似文献