共查询到19条相似文献,搜索用时 32 毫秒
1.
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
2.
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
3.
4.
本文讨论条件矩限制回归模型的参数估计.使用非参数估计方法给出条件密度和条件均值的估计,在此基础上给出参数的广义矩估计.进一步讨论了估计的渐近正态性. 相似文献
5.
6.
广义帕累托分布(GPD)在极值统计的POT模型中常常被用来逼近超过阈值u的超出量X_i-u的分布.
为解决经典估计方法存在的问题, Zhang (Zhang J, Likelihood moment estimation for the generalized Pareto distribution, Aust N Z J Stat,
2007, 49:69--77) 对两参数GPD (GP2)提出一种新的估计方法------似然矩估计(LM),
它容易计算且具有较高的渐近有效性. 本文将此方法从两参数的情形推广到三参数GPD (GP3),
结果表明尺度参数和形状参数估计的渐近性质与以上所提到的文章完全相同. 针对GP3的LM估计也具有总是存在、易于计算以及
对绝大多数的形状参数具有接近于最小的偏差和均方误差的特点. 相似文献
7.
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
8.
王炳章 《数学的实践与认识》2021,(1):258-264
研究了柯西分布的参数估计问题,给出了位置参数的最小一乘估计和尺度参数的低阶矩估计.证明了柯西分布位置参数的最小一乘估计具有渐近无偏性与强相合性;尺度参数的低阶矩估计具有强相合性. 相似文献
9.
Cox-Ingersoll-Ross模型的统计推断 总被引:1,自引:0,他引:1
本文研究了Cox—Ingersoll—Ross模型的统计推断问题.给出了CIR过程的平稳均值m与平稳方差v的矩估计,并利用m和v给出了CIR过程中尺度参数α与波动率β之间的关系,讨论了参数α的条件矩估计和渐近极大似然估计.并通过数值模拟对条件矩估计,渐近极大似然估计这两种方法作了比较. 相似文献
10.
讨论了在定时截尾样本下三参数威布尔分布的矩估计问题,得到了在定时截尾样本下三参数威布尔分布的矩估计方程,进而得截尾样本的矩估计(MME).用随机模拟方法表明此矩估计方法有较好的性质. 相似文献
11.
Extreme value theory has been widely used in analyzing catastrophic risk. The theory mentioned that the generalized Pareto distribution (GPD) could be used to estimate the limiting distribution of the excess value over a certain threshold; thus the tail behaviors are analyzed. However, the central behavior is important because it may affect the estimation of model parameters in GPD, and the evaluation of catastrophic insurance premiums also depends on the central behavior. This paper proposes four mixture models to model earthquake catastrophic loss and proposes Bayesian approaches to estimate the unknown parameters and the threshold in these mixture models. MCMC methods are used to calculate the Bayesian estimates of model parameters, and deviance information criterion values are obtained for model comparison. The earthquake loss of Yunnan province is analyzed to illustrate the proposed methods. Results show that the estimation of the threshold and the shape and scale of GPD are quite different. Value-at-risk and expected shortfall for the proposed mixture models are calculated under different confidence levels. 相似文献
12.
Traditional estimations of parameters of
the generalized Pareto distribution (GPD) are generally constrained
by the shape parameter of GPD. Such as: the method-of-moments (MOM),
the probability-weighted moments (PWM), L-moments (LM), the maximum
likelihood estimation (MLE) and so on. In this paper we use the fact
that GPD can be transformed into the exponential distribution and
use the results of parameters estimation for the exponential
distribution, than we propose parameters estimators of the
two-parameter or three-parameter GPD by the least squares method.
Some asymptotic results are provided and the proposed method not
constrained by the shape parameter of GPD. A simulation study is
carried out to evaluate the performance of the proposed method and
to compare them with other methods suggested in this paper. The
simulation results indicate that the proposed method performs better
than others in some common situation. 相似文献
13.
Nader Tajvidi 《Extremes》2003,6(2):111-123
The generalized Pareto distribution (GPD) is a two-parameter family of distributions which can be used to model exceedances over a threshold. We compare the empirical coverage of some standard bootstrap and likelihood-based confidence intervals for the parameters and upper p-quantiles of the GPD. Simulation results indicate that none of the bootstrap methods give satisfactory intervals for small sample sizes. By applying a general method of D. N. Lawley, correction factors for likelihood ratio statistics of parameters and quantiles of the GPD have been calculated. Simulations show that for small sample sizes accuracy of confidence intervals can be improved by incorporating the computed correction factors to the likelihood-based confidence intervals. While the modified likelihood method has better empirical coverage probability, the mean length of produced intervals are not longer than corresponding bootstrap confidence intervals. This article also investigates the performance of some bootstrap methods for estimation of accuracy measures of maximum likelihood estimators of parameters and quantiles of the GPD. 相似文献
14.
Ouyang Zisheng Xie Chi 《高校应用数学学报(英文版)》2006,21(1):21-29
How to choose an optimal threshold is a key problem in the generalized Pareto distribution (GPD) model. This paper attains the exact threshold by testing for GPD,and shows that GPD model allows the actuary to easily estimate high quantiles and the probable maximum loss from the medical insurance claims data. 相似文献
15.
Tail data are often modelled by fitting a generalized Pareto distribution (GPD) to the exceedances over high thresholds. In practice, a threshold is fixed and a GPD is fitted to the data exceeding . A difficulty in this approach is the selection of the threshold above which the GPD assumption is appropriate. Moreover the estimates of the parameters of the GPD may depend significantly on the choice of the threshold selected. Sensitivity with respect to the threshold choice is normally studied but typically its effects on the properties of estimators are not accounted for. In this paper, to overcome the difficulties of the fixed-threshold approach, we propose to model extreme and non-extreme data with a distribution composed of a piecewise constant density from a low threshold up to an unknown end point and a GPD with threshold for the remaining tail part. Since we estimate the threshold together with the other parameters of the GPD we take naturally into account the threshold uncertainty. We will discuss this model from a Bayesian point of view and the method will be illustrated using simulated data and a real data set. 相似文献
16.
How to choose an optimal threshold is a key problemin the generalized Pareto distribution (GPD) model.This paper attains the exactthreshold by testing for GPD,and shows that GPD model allows the actuary to easily estimate high quantiles and the probable maximum loss from the medical insurance claims data. 相似文献
17.
René Michel 《Extremes》2007,10(3):83-107
The investigation of multivariate generalized Pareto distributions (GPDs) has begun only recently. For further progress with
these distributions simulation methods are an important part. We describe several methods of simulating GPDs, beginning with
an efficient method for the logistic GPD. The algorithm is based on the Shi transformation, which was already used for the
simulation of multivariate extreme value distributions (EVDs) of logistic type. In the sequel another algorithm is presented
simulating a broader class of GPDs. Due to its numerical complexity it is only practicably applicable in low dimensions. A
method is given to generate unconditional GPD random vectors from conditionally GPD distributed random vectors. A short application
of the simulation methods in the analysis of a real hydrological data set concludes the article. The simulation algorithms
are available on the author’s home page .
相似文献
18.
19.
We present a quasi-conjugate Bayes approach for estimating Generalized Pareto Distribution (GPD) parameters, distribution
tails and extreme quantiles within the Peaks-Over-Threshold framework. Damsleth conjugate Bayes structure on Gamma distributions
is transfered to GPD. Posterior estimates are then computed by Gibbs samplers with Hastings-Metropolis steps. Accurate Bayes
credibility intervals are also defined, they provide assessment of the quality of the extreme events estimates. An empirical
Bayesian method is used in this work, but the suggested approach could incorporate prior information. It is shown that the
obtained quasi-conjugate Bayes estimators compare well with the GPD standard estimators when simulated and real data sets
are studied.
AMS 2000 Subject Classification Primary—62G32, 62F15, 62G09 相似文献