农作物单产的最大熵分布及在费率厘定上的应用

农作物单产分布的确定是农业保险中费率厘定的基础。本文引入最大熵原理,基于最大熵优化模型得出农作物单产的最大熵分布,并以此进行费率厘定。同时以辽宁省主要作物水稻、玉米、大豆和花生为例,确定了该四种农作物的费率,分别为4.45%、6.77%、6.34%、6.43%。结果表明:利用最大熵分布理论进行费率厘定不需要事先假定农作物单产分布的形式,而且考虑了更多作物单产分布的信息,为农业保险费率的合理精算提供一种新的可供选择的方法,有助于农业风险决策的科学化。     

正态分布和瑞利分布混合情形下的参数估计及分类问题

学者往往用单一的分布模拟和拟合杂波,如正态分布、瑞利分布和威布尔分布等。然而在实际中,雷达杂波由多种类型的杂波组成,单一分布通常不能精确刻画雷达杂波规律,因此,应用混合分布模型对雷达杂波数据建模更准确。本文考虑用正态分布和瑞利分布的混合分布拟合杂波,并应用矩估计方法和基于EM算法的极大似然估计方法估计模型参数,最后,应用最大后验概率分类准则验证2种估计方法的分类准确率。通过数据模拟,得出极大似然估计的效果和分类准确率都要优于矩估计的估计效果和分类准确率。     

Lomax分布极大似然估计的两点研究

本文研究了Lomax分布参数极大似然估计的存在性和估计量的收敛性问题.利用严格的分析法和中心极限定理,获得了Lomax分布极大似然估计的存在性和估计量的渐近正态分布的结果,进一步推广到了有缺失数据的两个Lomax总体中,参数的极大似然估计有强相合性和渐近正态性.     

Non-Parametric Estimation of the Limit Dependence Function of Multivariate Extremes

This paper presents a new estimation procedure for the limit distribution of the maximum of a multivariate random sample. This procedure relies on a new and simple relationship between the copula of the underlying multivariate distribution function and the dependence function of its maximum attractor. The obtained characterization is then used to define a class of kernel-based estimates for the dependence function of the maximum attractor. The consistency and the asymptotic distribution of these estimates are considered.     

指数分布抽样基本定理及在三参数一般指数分布参数估计中的应用

讨论三参数一般指数分布的参数估计,首先讨论了三参数一般指数分布参数的最大似然估计的求解问题,当其中参数α=1时,应用指数分布抽样基本定理,得到了三参数一般指数分布其它参数的一致最小方差无偏估计;并且由此给出求解三参数一般指数分布参数最大似然估计的迭代方法,得到了三参数一般指数分布参数最大似然估计的近似值,给出了模拟结果以说明迭代方法的收敛性;并以相关文献的观察数据作为样本,得到了三参数一般指数分布的参数估计,从而说明了迭代方法的有效性.     

基于最大熵的延迟启动/关闭N策略M/G/1可修排队稳态队长分布

研究具有延迟启动-关闭的N策略M/G/1可修排队系统,利用最大熵方法导出稳态队长分布的解析解,进一步得到基于最大熵的顾客平均等待时间.通过比较顾客的平均等待时间来检验最大熵方法的精度,结果表明基于最大熵方法得到的稳态队长分布是相当精确的.     

The maximum size of the planar sections of random spheres and its application to metallurgy

A theorem of this paper proves that if the size distribution of random spheres is generalized gamma, its Wicksell transform and other related distributions belong to the domain of attraction of the Gumbel distribution. The theorem also shows the attraction coefficients of the distributions. The fatigue strength of high-strength steel is closely related to the maximum size of nonmetallic inclusions in the region of maximum stress of the steel. Murakami and others developed a method, making use of the Gumbel QQ-plot, for predicting the maximum size from the size distribution of inclusion circles in microscopic view-fields. Based on the Gumbel approximation of the maximum of wicksell transforms, a modified and extended version of Murakami's method is justified, and its performance is evaluated by simulation.     

Pareto分布环境因子的估计及其应用

给出了Pareto分布环境因子的定义,讨论了在定数截尾样本下Pareto分布环境因子的极大似然估计和修正极大似然估计,并尝试把环境因子用于可靠性评估中.最后运用Monte Carlo方法对极大似然估计,修正极大似然估计和可靠性指标的均方误差(MSE),进行了模拟比较,结果表明修正极大似然估计优于极大似然估计且考虑环境因子的可靠性评估结果较好.     

Estimation of the Extreme Flow Distributions by Stochastic Models

The t-year event is a commonly used characteristic to describe the extreme flood peak in hydrological designs. The annual maximum series (AMS) and the partial duration series (PDS) are two basic approaches in flood analyses. In this paper, we first derive the distribution of the maximum extreme or the joint distribution of two or more maximum extremes from historical records based on a stochastic model, and then estimate statistical characteristics, including the t-year event, from the distribution. In addition to the two classical approaches (AMS and PDS), two additional approaches are proposed for estimating the unknown parameters in this paper. The first one uses two or more annual maximums (MAMS) as the sample to estimate the distribution of the maximum extremes. The second one uses multi-variate shock model to estimate the distribution of the maximum extremes for a multi-modal streamflow. The distribution of the extreme streamflow and the associated characteristics in the Bird Creek in Avant, Oklahoma, in the St. Johns River in Deland, Florida, and in the West Walker River in Coleville, California are estimated by using the stochastic model. To investigate further the performance of the estimation, the stochastic models based on AMS, MAMS and PDS related are also applied to the simulated data. The results show that the stochastic model and the related methods are reliable.     

离散型与连续型分布互为对偶的根源

互为对偶的离散型分布与连续型分布,可以看作是由同一个函数——源函数产生的。源函数的正线性组合、乘积和负导数,仍然是源函数。源函数揭示了互为对偶的分布的分布函数之间的相互关系,并能用来求随机变量的数字特征、特征函数、概率母函数、分布的最大值和参数的极大似然估计.     

On the maximum deviation between the histogram and the underlying density

Summary The limiting joint distribution of the location and size of the maximum deviation between the historgram and the underlying density is derived. For smooth densities, the location and size of the maximum are asymptotically independent. The size has a limiting double-exponential distribution and the location has a limiting normal distribution.Research partially supported by NSF grant MCS-80-02535Research partially supported by NSF grant MCS-77-16974     

Statistics of the three-parameter weibull distribution

We consider the estimation of the parameters of the three-parameter Weibull distribution, with particular emphasis on the unknown endpoint of the distribution. We summarize recent results on the asymptotic behaviour of maximum likelihood estimators. We continue with an example in which maximum likelihood and Bayesian estimators arc compared. We conclude that there are practical advantages to the Bayesian approach, but the study also suggests ways in which the maximum likelihood analysis may be improved.     

一种具有“浴盆”失效率的寿命分布的性质与统计分析

给出了一种具有"浴盆"失效率的寿命分布形式,讨论了该寿命分布密度函数、失效率函数的图像特征,证明了其高阶矩的存在性,讨论了"浴盆"底部的宽度以及寿命分布中参数的含义。研究了该寿命分布参数的极大似然估计、最小二乘估计,通过Monte Carlo模拟认为极大似然估计更为精确。论文最后通过四个具体实例说明该寿命分布的合理性,具有实际应用价值。     

Distributional expansion of maximum from logarithmic general error distribution

Logarithmic general error distribution is an extension of lognormal distribution. In this paper, with optimal norming constants the higher-order expansion of distribution of partial maximum of logarithmic general error distribution is derived.     

A note on the Sarmanov bivariate distributions

We investigate the maximum correlation for Sarmanov bivariate distributions with fixed marginals and strengthen the existing results in the literature. The improvement in the maximum correlation is significant. A characterization of the Sarmanov distribution via chi-square divergence is also given. This extends Nelsen [13] result about the Farlie-Gumbel-Morgenstern (FGM) distribution.     

A Formula for the Tail Probability of a Multivariate Normal Distribution and Its Applications

An exact asymptotic formula for the tail probability of a multivariate normal distribution is derived. This formula is applied to establish two asymptotic results for the maximum deviation from the mean: the weak convergence to the Gumbel distribution of a normalized maximum deviation and the precise almost sure rate of growth of the maximum deviation. The latter result gives rise to a diagnostic tool for checking multivariate normality by a simple graph in the plane. Some simulation results are presented.     

Asymptotic properties of conditional maximum likelihood estimator in a certain exponential model

The conditional maximum likelihood estimator is suggested as an alternative to the maximum likelihood estimator and is favorable for an estimator of a dispersion parameter in the normal distribution, the inverse-Gaussian distribution, and so on. However, it is not clear whether the conditional maximum likelihood estimator is asymptotically efficient in general. Consider the case where it is asymptotically efficient and its asymptotic covariance depends only on an objective parameter in an exponential model. This remand implies that the exponential model possesses a certain parallel foliation. In this situation, this paper investigates asymptotic properties of the conditional maximum likelihood estimator and compares the conditional maximum likelihood estimator with the maximum likelihood estimator. We see that the bias of the former is more robust than that of the latter and that two estimators are very close, especially in the sense of bias-corrected version. The mean Pythagorean relation is also discussed.     

The Maximum Surplus Distribution before Ruin in an Erlang（n） Risk Process Perturbed by Diffusion

In this paper, we consider the distribution of the maximum surplus before ruin in a generalized Erlang(n) risk process (i.e., convolution of n exponential distributions with possibly different parameters) perturbed by diffusion. It is shown that the maximum surplus distribution before ruin satisfies the integro-differential equation with certain boundary conditions. Explicit expressions are obtained when claims amounts are rationally distributed. Finally, the surplus distribution at the time of ruin and the surplus distribution immediately before ruin are presented.     

The localisation of the discharge channel in a glow discharge

The localisation of the discharge channel under the conditions of a glow discharge in air, at different distances from the cathode and at various points in the cathode dark space for different voltages, has been studied by measuring the radial distribution of the light intensity in the discharge channel. It has been shown that the radial ion distribution which has a flat maximum at lower voltages changes over into an approximately Gaussian one as the discharge voltage is increased. In the former case the width of the flat maximum decreases as the ion-channel proceeds towards the cathode. At higher voltages (~ 6 kV.) the flat maximum type of distribution in the ion-channel progressively changes over into the Gaussian as the channel approaches the cathode.     

参变极值问题的信息凝聚分布与Boltzmann极大熵函数

该文利用Ｂｏｌｔｚｍａｎｎ 熵概念给出了参变极值问题最优解的一种积分极限表达式和极值函数的极大熵函数,讨论了它们一致收敛性的要求并给出了极大熵函数一致收敛的一个充分条件,将之应用到全局最优解问题得到了全局最优解和最优值的一种显表示,最后还探讨了极大熵函数在一类双层规划问题求解中的应用．