Design of progressively censored group sampling plans for Weibull distributions: An optimization problem

Optimization algorithms provides efficient solutions to many statistical problems. Essentially, the design of sampling plans for lot acceptance purposes is an optimization problem with several constraints, usually related to the quality levels required by the producer and the consumer. An optimal acceptance sampling plan is developed in this paper for the Weibull distribution with unknown scale parameter. The proposed plan combines grouping of items, sudden death testing in each group and progressive group removals, and its decision criterion is based on the uniformly most powerful life test. A mixed integer programming problem is first solved for determining the minimum number of failures required and the corresponding acceptance constant. The optimal number of groups is then obtained by minimizing a balanced estimation of the expected test cost. Excellent approximately optimal solutions are also provided in closed-forms. The sampling plan is considerably flexible and allows to save experimental time and cost. In general, our methodology achieves solutions that are quite robust to small variations in the Weibull shape parameter. A numerical example about a manufacturing process of gyroscopes is included for illustration.     

DERIVATION OF TWO WELL‐BEHAVED THEORETICAL CONTAGION INDICES AND THEIR SAMPLING PROPERTIES AND APPLICATION FOR ASSESSING FOREST LANDSCAPE DIVERSITY

Abstract Studies of spatial patterns of landscapes are useful to quantify human impact, predict wildlife effects, or describe variability of landscape features. A common approach to identify and quantify landscape structure is with a landscape scale model known as a contagion index. A contagion index quantifies two distinct components of landscape diversity: composition and configuration. Some landscape ecologists promote the use of relative contagion indices. It is demonstrated that relativized contagion indices are mathematically untenable. Two new theoretical contagion indices, Γ₁ and Γ₂ , are derived using a mean value approach (i.e., statistical expected value) instead of entropy. Behavior of Γ₁ and Γ₂ was investigated with simulated random, uniform, and aggregated landscapes. They are shown to be well‐behaved and sensitive to composition and configuration. Distributional properties of and are derived. They are shown to be asymptotically unbiased, consistent, and asymptotically normally distributed. Variance formulas for and are developed using the delta method. The new index models are used to examine landscape diversity on three physiographic provinces in Alabama by analyzing the pattern and changes in forest cover types over the recent past. In comparing and , use of in analysis of variance gave a more conservative test of contagion.     

按揭支付的单调性分析

考虑了基于随机提前偿付的按揭支付的期望收入或损失的分析模型,模型具有和提前偿付的概率分布无关的一些单调特性,揭示了潜在的异于传统的按揭风险控制思路,可以支持新颖支付模式的研发,并构成按揭风险治理的有力补充.     

A robust von Neumann minimax theorem for zero-sum games under bounded payoff uncertainty

The celebrated von Neumann minimax theorem is a fundamental theorem in two-person zero-sum games. In this paper, we present a generalization of the von Neumann minimax theorem, called robust von Neumann minimax theorem, in the face of data uncertainty in the payoff matrix via robust optimization approach. We establish that the robust von Neumann minimax theorem is guaranteed for various classes of bounded uncertainties, including the matrix 1-norm uncertainty, the rank-1 uncertainty and the columnwise affine parameter uncertainty.     

On the Decay of Crossing Numbers of Sparse Graphs

Richter and Thomassen proved that every graph has an edge e such that the crossing number of is at least . Fox and Cs. Tóth proved that dense graphs have large sets of edges (proportional in the total number of edges) whose removal leaves a graph with crossing number proportional to the crossing number of the original graph; this result was later strenghthened by ?erný, Kyn?l, and G. Tóth. These results make our understanding of the decay of crossing numbers in dense graphs essentially complete. In this article we prove a similar result for large sparse graphs in which the number of edges is not artificially inflated by operations such as edge subdivisions. We also discuss the connection between the decay of crossing numbers and expected crossing numbers, a concept recently introduced by Mohar and Tamon.     

常数分红界下两离散相依险种风险模型的分红问题

主要研究了常数分红界下两离散相依险种风险模型的分红问题.模型假定一个险种的主索赔以一定的概率引起另外一险种的副索赔,且副索赔可能延迟发生,推导了到破产前一时刻为止累积分红折现均值满足的差分方程,并得到了特殊索赔额下累积分红折现均值的具体表达式,最后结合实际例子进行了数值模拟.     

具有常数利率的延迟更新风险模型

考虑常数利率情形下的延迟更新风险过程．得到了该延迟更新风险模型下的Gerber-Shiu期望折现罚金函数的表达式,并得到了常数利率下的一种特殊的延迟更新风险模型的破产概率的显示表达式.     

The Pricing of Deposit Insurance Considering Regulatory Capital and Bankruptcy Cost

We develop a deposit insurance pricing model that explicitly considers regulatory capital and bankruptcy costs. Based on the pricing deposit insurance model, we calculate the deposit insurance premiums of China's 16 listed banks with time span of 2011 to 2017 in this paper. The results demonstrate that the deposit insurance premiums of state-owned banks is lower than joint-stock commercial banks and city commercial banks, however, the deposit insurance premiums of joint-stock commercial banks is higher than city commercial banks. Numerical simulation shows that, ceteris paribus, the value of deposit insurance decreases with regulatory capital ratios and the insured deposits ratios, but it increases with interest rate and bankruptcy costs.