On a class exhibiting trend change in average failure rate

Abstract

Weak convergence and moment convergence issues are investigated for the New Better than Average Failure Rate (NBAFR) family (introduced by Loh (1984 Loh, W. Y. 1984. A new generalization of the class of NBU distributions. IEEE Transactions on Reliability R-33 :97–113[Crossref], [Web of Science ®] , [Google Scholar])). We explore the validity of these results in the context of a more general ageing class that we introduce. We prove some new properties of this class and derive its interrelationships with other non-monotonic ageing families. Reliability and moment bounds are obtained and an interesting characterization of exponentiality is proved. Special cases of our results lead to new theorems for the NBAFR class. Finally weak convergence and related issues are established for this class.     

SHOULD WE ESTIMATE THE PROBABILITY OF CORRECT SELECTION?

Various authors, given k location parameters, have considered lower confidence bounds on (standardized) dserences between the largest and each of the other k - 1 parameters. They have then used these bounds to put lower confidence bounds on the probability of correct selection (PCS) in the same experiment (as was used for finding the lower bounds on differences). It is pointed out that this is an inappropriate inference procedure. Moreover, if the PCS refers to some later experiment it is shown that if a non-trivial confidence bound is possible then it is already possible to conclude, with greater confidence, that correct selection has occurred in the first experiment. The short answer to the question in the title is therefore ‘No’, but this should be qualified in the case of a Bayesian analysis.     

Uncertain Numbers and Uncertainty in the Selection of Input Distributions—Consequences for a Probabilistic Risk Assessment of Contaminated Land

Risks from exposure to contaminated land are often assessed with the aid of mathematical models. The current probabilistic approach is a considerable improvement on previous deterministic risk assessment practices, in that it attempts to characterize uncertainty and variability. However, some inputs continue to be assigned as precise numbers, while others are characterized as precise probability distributions. Such precision is hard to justify, and we show in this article how rounding errors and distribution assumptions can affect an exposure assessment. The outcome of traditional deterministic point estimates and Monte Carlo simulations were compared to probability bounds analyses. Assigning all scalars as imprecise numbers (intervals prescribed by significant digits) added uncertainty to the deterministic point estimate of about one order of magnitude. Similarly, representing probability distributions as probability boxes added several orders of magnitude to the uncertainty of the probabilistic estimate. This indicates that the size of the uncertainty in such assessments is actually much greater than currently reported. The article suggests that full disclosure of the uncertainty may facilitate decision making in opening up a negotiation window. In the risk analysis process, it is also an ethical obligation to clarify the boundary between the scientific and social domains.     

Statistical estimation of internal available bandwidth

This paper presents a method for using end-to-end available bandwidth measurements in order to estimate available bandwidth on individual internal links. The basic approach is to use a power transform on the observed end-to-end measurements, model the result as a mixture of spatially correlated exponential random variables, carryout estimation by moment methods, then transform back to the original variables to get estimates and confidence intervals for the expected available bandwidth on each link. Because spatial dependence leads to certain parameter confounding, only upper bounds can be found reliably. Simulations with ns2 show that the method can work well and that the assumptions are approximately valid in the examples.     

全面建设小康社会与加快民族地区发展

民族地区地域广大 ,资源丰富 ,潜在市场广阔 ,在全面建设小康社会中具有十分重要的战略地位。同时 ,民族地区经济社会发展的滞后又给全面建设小康社会带来了许多困难。只有切实克服这些困难和问题 ,才能有效地推进全面建设小康社会的伟大事业。应加大国家的扶持力度 ,认真贯彻党的民族政策 ,解放思想 ,发挥优势 ,依靠科技进步 ,采取一系列措施 ,实现民族地区的跨越式发展。     

跨跃式发展是黑龙江省民族地区全面建设小康社会的关键

本文在分析黑龙江省民族地区社会经济发展存在的差距基础之上,提出跨跃式发展是黑龙江省实现全面建设小康社会的关键,同时就促使民族地区社会经济跨跃式发展阐述了自己的看法。     

论我国民族地区的跨越式发展

跨越式发展是民族发展的一种形式,也是加快我国民族地区经济文化发展的有效途径。文章结合我国国情,分析了我国民族地区要实现跨越式发展的原因和条件,并提出了具体措施和建议。     

文献型翻译和工具型翻译——析《Moment in Peking》中社会文化因素的翻译策略

通过对功能主义翻译目的论提出的文献型翻译和工具型翻译进行阐释,结合林语堂Moment in Peking《京华烟云》中社会文化因素的翻译策略,比较这两种翻译策略在文化传播中的作用。指出以传播中国文化为目的时,译者宜主要采用文献型翻译;以提高译文在西方读者中的可读性为目的时,宜主要采用工具型翻译。     

Order statistics from trivariate normal and -distributions in terms of generalized skew-normal and skew- distributions

We consider here a generalization of the skew-normal distribution, GSN(λ₁,λ₂,ρ), defined through a standard bivariate normal distribution with correlation ρ, which is a special case of the unified multivariate skew-normal distribution studied recently by Arellano-Valle and Azzalini [2006. On the unification of families of skew-normal distributions. Scand. J. Statist. 33, 561–574]. We then present some simple and useful properties of this distribution and also derive its moment generating function in an explicit form. Next, we show that distributions of order statistics from the trivariate normal distribution are mixtures of these generalized skew-normal distributions; thence, using the established properties of the generalized skew-normal distribution, we derive the moment generating functions of order statistics, and also present expressions for means and variances of these order statistics.Next, we introduce a generalized skew-t_ν distribution, which is a special case of the unified multivariate skew-elliptical distribution presented by Arellano-Valle and Azzalini [2006. On the unification of families of skew-normal distributions. Scand. J. Statist. 33, 561–574] and is in fact a three-parameter generalization of Azzalini and Capitanio's [2003. Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution. J. Roy. Statist. Soc. Ser. B 65, 367–389] univariate skew-t_ν form. We then use the relationship between the generalized skew-normal and skew-t_ν distributions to discuss some properties of generalized skew-t_ν as well as distributions of order statistics from bivariate and trivariate t_ν distributions. We show that these distributions of order statistics are indeed mixtures of generalized skew-t_ν distributions, and then use this property to derive explicit expressions for means and variances of these order statistics.