单峰偏好下马斯金单调性与联盟防策略的等价性

本文证明了在单峰偏好域上Maskin单调性与防策略条件是等价的,并进一步证明了Maskin单调性与联盟防策略是等价的.从而推广了Muller-Satterthwaite(1977)在无限制强序域上得到的结论.在此基础上,利用Mollin(1980)在单峰偏好域上提出的防策略社会选择函数特征化定理,证明了在单峰偏好域上能够突破Muller-Satterthwaite不可能性定理所预示的消极结论.     

On the Moments of Overflow and Freed Carried Traffic for the GI/M/C/0 System

In circuit-switched networks call streams are characterized by their mean and peakedness (two-moment method). The GI/M/C/0 system is used to model a single link, where the GI-stream is determined by fitting moments appropriately. For the moments of the overflow traffic of a GI/M/C/0 system there are efficient numerical algorithms available. However, for the moments of the freed carried traffic, defined as the moments of a virtual link of infinite capacity to which the process of calls accepted by the link (carried arrival process) is virtually directed and where the virtual calls get fresh exponential i.i.d. holding times, only complex numerical algorithms are available. This is the reason why the concept of the freed carried traffic is not used. The main result of this paper is a numerically stable and efficient algorithm for computing the moments of freed carried traffic, in particular an explicit formula for its peakedness. This result offers a unified handling of both overflow and carried traffics in networks. Furthermore, some refined characteristics for the overflow and freed carried streams are derived.     

Markov inequalities on partially ordered spaces

Let X(ω) be a random element taking values in a linear space $\text{X}$ endowed with the partial order ≤; let $\text{G}$₀ be the class of nonnegative order-preserving functions on $\text{X}$ such that, for each g∈$\text{G}$₀, E[g(X)] is defined; and let $\text{G}$₁?$\text{G}$₀ be the subclass of concave functions. A version of Markov's inequality for such spaces in P(X ≥ x) ≤ inf_$\text{G}$0E[g(X)]/g(x). Moreover, if E(X) = ξ is defined and if Jensen's inequality applies, we have a further inequality P(X≥x) ≤ inf_$\text{G}$1E[g(X)]/g(x) ≤ inf_$\text{G}$1g(ξ)/g(x). Applications are given using a variety or orderings of interest in statistics and applied probability.     

Influence of the prior distribution on the risk of the Bayes rule

The risk influence function is defined as the directional derivative of the risk of the Bayes rule. The properties of this function are studied and the relationship between unimodal prior distribution and the shape of the frequentist risk of the corresponding Bayes procedure is examined.     

Kurtosis: a forgotten moment

The treatment of kurtosis in textbooks is both sparse and contradictory with applications rarely discussed. To address this, an easily understood definition of kurtosis is introduced and important applications are demonstrated. Two different approaches to teaching kurtosis are presented based on a financial application.     

Inequalities for probability contents of convex sets via geometric average

It is shown that: If (X₁, X₂) is a permutation invariant central convex unimodal random vector and if A is a symmetric (about 0) permutation invariant convex set then P{(aX₁, X₂/a) A} is nondecreasing as a varies from )+ to 1 and is non-increasing as a varies from 1 to ∞ (that is, P{(a₁X₁, a₂X₂) ε A} is a Schur-concave function of (log a₁, log a₂). Some extensions of this result for the n-dimensional case are discussed. Applications are given for elliptically contoured distributions and scale parameter families.     

Individual Overflow and Freed Carried Traffics for a Link with Trunk Reservation

Two traffic streams Φ₁, Φ₂ are offered a link. The calls of Φ_i require exponential holding times with parameter μ and are accepted if less than C_i trunks are occupied. Approximating the Φ_i by appropriate renewal processes meeting their first two moments, defined as the moments of the numbers of calls in virtual links of infinite capacity to which the traffic streams as freed traffics are virtually directed and where the calls get fresh exponential i.i.d. holding times with parameter μ, stable recursive algorithms of complexity O(max (C₁,C₂)) are derived for the first two defined as above moments of the individual overflow and freed carried traffics. The results offer a unified handling of both overflow and carried traffics in circuit switched networks with trunk reservation, providing a basis for new two-moment network dimensioning algorithms.This work was supported by a grant from the Siemens AG.