Statistical Analysis Technique of Two-parameter Generalized Exponential Sum Distribution

A new life distribution is proposed, known as ``two-parameter generalized exponential sum distribution". We study the density function and failure rate function, the average failure rate function, the image features and the numerical characteristics of the mean residual life of the distribution. Several methods of calculating point estimation of parameters are discussed. Through the Monte-Carlo simulation, we compare the precision of the point estimations. In our opinion, the best linear unbiased estimation is the most optimal solution of these methods. At the same time, several methods of calculating parameters of interval estimations are given. We also discuss the precision of interval estimations by Monte-Carlo simulation and use the best linear unbiased estimation and the best linear invariant estimation to construct interval estimations which are better than other estimation method. Finally, several simulation examples and a case of maintaining tanks is used to illustrate the application of the methods presented in this paper.     

Statistical analysis of two-parameter generalized Birnbaum-Saunders Cauchy distribution

The image features of density function and failure rate function are studied in detail for two-parameter generalized Birnbaum-Saunders Cauchy fatigue life distribution. The logarithmic moment estimation and other two point estimations of parameters are proposed under full sample, and the precisions of point estimations are investigated by Monte-Carlo simulations. The approximate interval estimations of parameters are given by using Taylor expansion, and the precisions of approximate interval estimations are investigated by Monte-Carlo simulations. Finally, several examples show the feasibility of the methods.     

多个偏正态总体共同位置参数的Bootstrap置信区间

该文基于Bootstrap 方法研究多个偏正态总体共同位置参数的区间估计和假设检验问题.首先,分别给出未知参数的矩估计和极大似然估计.其次,将徐礼文[1]对多个正态总体共同均值的探讨推广到多个偏正态总体,进而构造共同位置参数的Bootstrap 置信区间和Bootstrap检验统计量.Monte Carlo模拟结果表明...     

定数截尾试验下两参数Weibull分布尺度参数的最优稳健Bayes估计

以Г-后验期望损失作为标准,研究了定数截尾试验下两参数W e ibu ll分布尺度参数θ的最优稳健Bayes估计问题.假设尺度参数θ的先验分布在分布族Г上变化,形状参数β已知时,在0-1损失下,得到了θ的最优稳健区间估计,在均方损失下得到θ的最优稳健点估计及区间估计;β未知时,得到了θ的最优稳健点估计及区间估计.最后给出了数值例子,说明了方法的有效性.     

Finding an inner estimation of the solution set of a fuzzy linear system

In this paper, we consider the problem of finding an inner estimation of the solution set of a fuzzy linear system with a real-valued coefficient matrix and a fuzzy-valued right-hand side vector. The proposed idea is based on the utilization of interval Gaussian elimination procedure to produce an inner estimation of the solutions set. To this end, firstly we apply interval Gaussian elimination procedure to obtain the solution set of a fuzzy linear system and secondly, by limiting it via solving a crisp linear system, we find an inner estimation of the solutions set, such that it satisfies the related fuzzy linear system. Finally, several numerical examples are given to show the efficiency and ability of our method.     

复合Linex对称损失下Kumaraswamy分布参数的Bayes估计

当参数的先验分布为伽玛分布时,在复合Linex对称损失函数下得到了Kumaraswamy分布参数θ的唯一的Bayes估计,多层Bayes估计和E-Bayes估计,并通过数值模拟说明了所给参数估计的稳健性和精确性.     

指数分布冷贮备系统产品的统计分析——转换开关完全可靠的情形

本文给出了全样本场合指数分布冷贮备系统产品在转换开关完全可靠的情形下参数的矩估计、极大似然估计、精确区间估计和近似区间估计,并通过大量Monte-Carlo模拟说明估计的精度。     

对数正态分布基于恒加试验的参数估计

讨论对数正态分布场合有非常数尺度参数恒加试验的参数估计,由最小均方误差准则导出基于完全样本恒加试验的点估计和近似区间估计.     

两种估计区间解法的讨论

依据等概率对称区间和等密度对称区间的概念引出两种估计区间求解方法,并通过两种方法推导证明了等密度对称区间即为最短估计区间.然后分别就F分布和χ2分布情形对这两种区间估计方法作以比较.比较发现,在同样条件下,等密度对称区间总比概率对称区间要短,并且随着自由度增加,两种区间趋于重合.     

随机右截尾情形下两个指数分布总体的比较

研究了随机右截尾情形下两个指数分布的参数估计.在两个指数分布的刻度参数都未知时,得到了两个指数分布的刻度参数的最大似然估计与参数比的区间估计.     

指数分布卷积形式参数的估计

本文研究指数分布卷积形式参数的点估计，区间估计以及经验分布函数与分布函数最大偏差的概率估计．     

Application of the modified operational matrices in multiterm variable‐order time‐fractional partial differential equations

In this paper, we present a novel discrete scheme based on Genocchi polynomials and fractional Laguerre functions to solve multiterm variable‐order time‐fractional partial differential equations (M‐V‐TFPDEs) in the large interval. In this purpose, the accurate modified operational matrices are constructed to reduce the problems into a system of algebraic equations. Also, the computational algorithm based on the method and modified operational matrices in the large interval is easily implemented. Furthermore, we discuss the error estimation of the proposed method. Ultimately, to confirm our theoretical analysis and accuracy of numerical approach, several examples are presented.     

Statistical Inference for the Parameter of Rayleigh Distribution Based on Progressively Typ e-I Interval Censored Sample

In this paper, the estimation of parameters based on a progressively type-I interval censored sample from a Rayleigh distribution is studied. Different methods of estimation are discussed. They include...     

Estimation of second-order properties from jittered time series

This paper considers spectral and autocovariance estimation for a zero-mean, band-limited, stationary process that has been sampled at time points jittered from a regular, equi-interval, sampling scheme. The case of interest is where the sampling scheme is near regular so that the jitter standard deviation is small compared to the sampling interval. Such situations occur with many time series collected in the physical sciences including, in particular, oceanographic profiles.Spectral estimation procedures are developed for the case of independent jitter and autocovariance estimation procedures for both independent and dependent jitter. These are typically modifications of general estimation procedures proposed elsewhere, but tailored to the particular jittered sampling scheme considered. The theoretical properties of these estimators are developed and their relative efficiencies compared.The properties of the jittered sampling point process are also developed. These lead to a better understanding, in this situation, of more general techniques available for processes sampled by stationary point processes.     

离散二元几何分布串联系统的参数估计

本文首次给出了二元几何分布的定义及其主要性质,并针对二元几何分布串联系统给出了参数的矩估计和极大似然估计,同时通过大量Monte-Carlo模拟考察了估计的精度,文章最后通过Monte-Carlo数值例子来说明方法的运用.     

熵损失函数下两参数指数威布尔分布尺度参数的Bayes估计

本文给定一截尾样本，在熵损失函数下，研究了两参数指数威布尔分布尺度参数在先验伽玛分布下的Bayes估计，并给出了该参数的Bayes区间估计。     

对数正态分布场合有非常数尺度参数恒加试验的参数估计

讨论了对数正态分布场合有非常数尺度参数恒加寿命试验的参数估计，导出了基于全样本和定数截尾样本恒加试验的点估计和近似区间估计。     

基于β分布的区间估计量化方法

区间估计是专家评价中的重要方法.针对区间估计的特点,构建了区间序列分布,分析了区间序列分布的特性和数字特征;结合β分布及其特性,提出了一种基于β分布的区间估计量化方法,着重探讨了用β分布拟合区间序列分布的原理方法;通过案例分析,表明该方法效果较好,并具有较好的普适性.     

n维球内均匀分布的参数估计

研究了n维球内均匀分布的参数的点估计与区间估计,利用次序统计量得到了球半径的最大似然估计,在此基础上构造了球半径的无偏估计,并且证明了该无偏估计的相合性.利用构造枢轴量的方法得到了球半径的最短置信区间.     

Confidence-based optimisation for the newsvendor problem under binomial,Poisson and exponential demand

We introduce a novel strategy to address the issue of demand estimation in single-item single-period stochastic inventory optimisation problems. Our strategy analytically combines confidence interval analysis and inventory optimisation. We assume that the decision maker is given a set of past demand samples and we employ confidence interval analysis in order to identify a range of candidate order quantities that, with prescribed confidence probability, includes the real optimal order quantity for the underlying stochastic demand process with unknown stationary parameter(s). In addition, for each candidate order quantity that is identified, our approach produces an upper and a lower bound for the associated cost. We apply this approach to three demand distributions in the exponential family: binomial, Poisson, and exponential. For two of these distributions we also discuss the extension to the case of unobserved lost sales. Numerical examples are presented in which we show how our approach complements existing frequentist—e.g. based on maximum likelihood estimators—or Bayesian strategies.