Measuring Kurtosis by Right and Left Inequality Orders

The question of how to measure kurtosis in both symmetric and asymmetric distributions is addressed using the kurtosis diagram of Zenga (2006 Zenga , M. ( 2006 ). Kurtosis . In : Kotz , S. , Read , C. B. , Balakrishnan , N. , Vidakovic , B. , eds. Encyclopedia of Statistical Sciences. 2nd ed . New York : John Wiley and Sons . [Google Scholar]). Kurtosis is related to inequality at either side of the median, and we establish a hierarchy of kurtosis orderings in which the kurtosis diagram stands at the weakest level. A sufficient condition for constructing kurtosis measures compatible with such ordering is provided. The merits of the proposed approach in both clarifying and formalizing the idea of kurtosis are evaluated and examples are discussed throughout.     

Functions of Concordance and Dependence with Related Measures

Some functions that serve as building blocks for construction of a wider range of modes of concordance and dependence are pointed. We probe into interplays of such modes. From the standpoint of their conformity to stochastic dominance ordering of distributions within a Fréchet class, all such derived modes display some parallelism under certain conditions. We finally suggest a novel numeric measure of dependence that covers similar existing measures in literature.     

Concomitants in a Sequence of Independent Nonidentically Distributed Random Vectors

ABSTRACT

Concomitants of order statistics are considered for the situation in which the random vectors (X ₁, Y ₁), (X ₂, Y ₂),…, (X _n , Y _n ) are independent but otherwise arbitrarily distributed. The joint and marginal distributions of the concomitants of order statistics and stochastic comparisons among the concomitants of order statistics are studied in this situation.     

An Analytical Investigation of the Bullwhip Effect

The Bullwhip Effect is problematic: order variability increases as orders propagate along the supply chain. The fundamental differential delay equations for a retailer's inventory reacting to a surge in demand are solved exactly. Much of the rich and complex inventory behavior is determined by the replenishment delay. The analytical solutions agree with numerical integrations and previous control theory results. Managerially useful ordering strategies are proposed. Exact expressions are derived for the retailer's orders to the manufacturer, and the Bullwhip Effect arises naturally. The approach is quite general and applicable to a wide variety of supply chain problems.     

The Impact of Information Sharing and Advance Order Information on a Supply Chain with Balanced Ordering

This paper considers a supply chain with one supplier and multiple retailers that face exogenous heterogeneous end‐customer demands, where all parties utilize base‐stock policies. Each retailer is restricted to order once in every order cycle and their orders are replenished in a balanced manner within the cycle. Our study investigates the impact of information sharing and advance order information (AOI) on the supply chain. We find that the supplier benefits from the two mechanisms via two important factors, the information about observed end‐customer demands and the decision on re‐establishing the replenishment sequence. We derive the supplier's optimal sequence for stochastically comparable end‐customer demands with AOI and propose a sequencing rule for the setting with information sharing. Our numerical study examines the cost impacts of two proposed mechanisms on the entire supply chain.     

Order Progress Information: Improved Dynamic Emergency Ordering Policies

Technologies such as radio‐frequency identification and global positioning systems can provide improved real‐time tracking information for products and replenishment orders along the supply chain. We call this type of visibility order progress information. In this paper, we investigate how order progress information can be used to improve inventory replenishment decisions. To this end, we examine a retailer facing a stochastic lead time for order fulfillment. We characterize a replenishment policy that is based on the classical (Q, R) policy and that allows for releasing emergency orders in response to the order progress information. We show that the optimal structure of this policy is given by a sequence of threshold values dependent on order progress information. In a numerical study we evaluate the cost savings due to this improved replenishment policy.     

基于顾客分类的生鲜农产品二次补货策略

零售商为弥补生鲜农产品新鲜度降低造成的顾客流失,选择在单销售期内二次补货,将新鲜产品和初始订货的非新鲜产品同时销售。但二次补货的新鲜产品会对初始订货产品形成需求挤兑。将顾客划分为三种类型:只购买新鲜产品、只够买折扣产品和两种产品都愿意购买,引入需求挤兑因子的概念,讨论了不同顾客类型下需求挤兑效应对零售商订货决策和利润的影响,并与单次订货策略做比较。结论表明,随着顾客对产品品质和新鲜度要求不断提高,二次补货策略能有效降低订货总量,提升零售商利润水平;不但优化了经济效益,更具有减少产品损耗和节约社会资源、增加消费者福利水平的社会效益。     

水平竞争条件下的供应链信息泄露策略

本文探讨非对称信息下,制造商针对议价能力不同的大型及小型零售商分别采用了收益共享、批发价合约时,大型零售商的市场信息被制造商泄露给竞争对手,从而对供应链产生的影响。通过对比有无信息泄露下各方成员的博弈过程,分析供应链信息泄露的原理;进而在制造商总是会泄露信息的前提下,构建基于信号传递的信息泄露下供应链成员决策模型,分别讨论分离均衡与混同均衡两种情形下,零售商的订货策略及其相应的收益。在此基础上进一步做出扩展,制造商有主动权以选择是否泄露信息的情况,对比分析零售商的策略选择问题。经过分析发现,出于自身利益的角度,制造商总是会泄露信息,从而导致供应链的整体利润下滑。对此,大型零售商的订货策略选择与市场需求的波动程度有关：波动较小则选择混同均衡;波动较大则选择分离均衡。特别地,当市场需求为低时,大型零售商的最优订货量会向下扭曲,即支付一定的“信息租金”作为应对信息泄露的代价。     

Preservation of generalized ageing classes on the residual life at random time

In this paper, we provide some new preservation properties of generalized ageing classes (s-IFR) on the residual life at random time, where s is a nonnegative integer. We also obtain bounds of the residual life at exponential random time. Results are expected to be useful in the reliability, queue theory and actuarial science.     

An adjusted cumulative Kullback-Leibler information with application to test of exponentiality

Abstract

In order to discriminate between two probability distributions extensions of Kullback–Leibler (KL) information have been proposed in the literature. In recent years, an extension called cumulative Kullback–Leibler (CKL) information is considered by authors which is closely related to equilibrium distributions. In this paper, we propose an adjusted version of CKL based on equilibrium distributions. Some properties of the proposed measure of divergence are investigated. A test of exponentiality based on the adjusted measure, is proposed. The empirical power of the presented test is calculated and compared with some existing standard tests of exponentiality. The results show that our proposed test, for some important alternative distributions, has better performance than some of the existing tests.