No‐Betting‐Pareto Dominance

We argue that the notion of Pareto dominance is not as compelling in the presence of uncertainty as it is under certainty. In particular, voluntary trade based on differences in tastes is commonly accepted as desirable, because tastes cannot be wrong. By contrast, voluntary trade based on incompatible beliefs may indicate that at least one agent entertains mistaken beliefs. We propose and characterize a weaker, No‐Betting, notion of Pareto domination which requires, on top of unanimity of preference, the existence of shared beliefs that can rationalize such preference for each agent.     

Two applications of a theorem of Dvoretsky, Wald, and Wolfovitz to cake division

In this note, we show that a partition of a cake is Pareto optimal if and only if it maximizes some convex combination of the measures used by those who receive the resulting pieces of cake. Also, given any sequence of positive real numbers that sum to one (which may be thought of as representing the players' relative entitlements), we show that there exists a partition in which each player receives either more than, less than, or exactly his or her entitlement (according to his or her measure), in any desired combination, provided that the measures are not all equal.     

Test of two hypotheses explaining the size of populations in a system of cities

Two classical hypotheses are examined about the population growth in a system of cities: Hypothesis 1 pertains to Gibrat's and Zipf's theory which states that the city growth–decay process is size independent; Hypothesis 2 pertains to the so-called Yule process which states that the growth of populations in cities happens when (i) the distribution of the city population initial size obeys a log-normal function, (ii) the growth of the settlements follows a stochastic process. The basis for the test is some official data on Bulgarian cities at various times. This system was chosen because (i) Bulgaria is a country for which one does not expect biased theoretical conditions; (ii) the city populations were determined rather precisely. The present results show that: (i) the population size growth of the Bulgarian cities is size dependent, whence Hypothesis 1 is not confirmed for Bulgaria; (ii) the population size growth of Bulgarian cities can be described by a double Pareto log-normal distribution, whence Hypothesis 2 is valid for the Bulgarian city system. It is expected that this fine study brings some information and light on other usually considered to be more pertinent countries of city systems.     

Inference and Optimal Design Based on Step—Partially Accelerated Life Tests for the Generalized Pareto Distribution under Progressive Type-I Censoring

Various types of failure, censored and accelerated life tests, are commonly employed for life testing in some manufacturing industries and products that are highly reliable. In this article, we consider the tampered failure rate model as one of such types that relate the distribution under use condition to the distribution under accelerated condition. It is assumed that the lifetimes of products under use condition have generalized Pareto distribution as a lifetime model. Some estimation methods such as graphical, moments, probability weighted moments, and maximum likelihood estimation methods for the parameters are discussed based on progressively type-I censored data. The determination of optimal stress change time is discussed under two different criteria of optimality. Finally, a Monte Carlo simulation study is carried out to examine the performance of the estimation methods and the optimality criteria.     

供应链中基于信息更新的订货时间及价格联合决策研究

文章考虑在信息可更新的情况下,由一个制造商和一个零售商组成的供应链中订货时间及价格的联合决策问题.在模型中,制造商为零售商提供多次订货时间选择及相应的订货价格,而零售商可以在销售季节开始前自由选择订货时间并享受相应的价格.文章以不同订货时间对信息更新程度的影响为着眼点,将订货时间作为内生决策变量,突破了已有文献中仅限于两次订货时间选择的局限,分别从集中决策和分散决策两个角度建立供应链节点企业的利润模型,并在分散决策情况下引入收益共享契约,寻找帕累托改进.最后通过数值试验证明了该模型的有效性.     

基于供应链的合作促销与定价问题

本文针对供应链中厂商和销售商之间的合作促销问题,使用博弈论的方法主要就最优的合作促销费用投入和定价进行了研究。首先讨论了传统的厂商为领导者,销售商为跟随者的情形,接着考虑到如今销售商地位的提高,对此进行了拓展,讨论了销售商为领导者的情形。最后以前两种情形为参照,建立了厂商和销售商之间Pareto改进的合作促销模型,并利用Nash讨价还价和效用理论得出了Pareto改进情形下的最优结果。     

An optimal sign test for one-sample bivariate location model using an alternative bivariate ranked-set sample

The aim of this paper is to find an optimal alternative bivariate ranked-set sample for one-sample location model bivariate sign test. Our numerical and theoretical results indicated that the optimal designs for the bivariate sign test are the alternative designs with quantifying order statistics with labels {((r+1)/2, (r+1)/2)}, when the set size r is odd and {(r/2+1, r/2), (r/2, r/2+1)} when the set size r is even. The asymptotic distribution and Pitman efficiencies of these designs are derived. A simulation study is conducted to investigate the power of the proposed optimal designs. Illustration using real data with the Bootstrap algorithm for P-value estimation is used.     

Triple sampling procedure for estimating the scale parameters of pareto distributions

This paper sheds light on the large sample performance of the three stage sam- pling procedure, as it pertains to estimating the scale parameter(s) of the Pareto distribution(s). This group sampling procedure merges the efficiency of the purely sequential procedure of Anscombe (1953) and Chow and Robbins (1965) with substan-tial savings in the number of sampling operations, as noted by Hall (1981). Both its simplicity and its economical features provide visible advantages over the one-by-one sampling as an alternative. In this paper we develop some asymptotic properties for the final stage sample size of the triple stage sampling originated by Hall (1981). These results are used to study both the point and the interval estimation problems for the scale parameters of the Pareto distributions. Since our results are asymptotic in nature, a simulation study is given to discuss the moderate sample size peformance of the proposed procedures.     

Bayesian estimation and prediction based on generalized Type-I hybrid censored sample

In this paper, we consider an exponential form for the underlying distributionand a conjugate prior, and develop a procedure for deriving the maximum likelihood and Bayesian estimators based on an observed generalized Type-I hybrid censored sample. The problems of predicting the future order statistics from the same sample and that from a future sample are also discussed from a Bayesian viewpoint. For the illustration of the developed results, the exponential and Pareto distributions are used as examples. Finally, two numerical examples are presented for illustrating all the inferential procedures developed here.