Rényi entropy of m-generalized order statistics

Abstract

Characterizing relations via Rényi entropy of m-generalized order statistics are considered along with examples and related stochastic orderings. Previous results for common order statistics are included.     

Inference and Decision Making for 21st-Century Drug Development and Approval

ABSTRACT

The cost and time of pharmaceutical drug development continue to grow at rates that many say are unsustainable. These trends have enormous impact on what treatments get to patients, when they get them and how they are used. The statistical framework for supporting decisions in regulated clinical development of new medicines has followed a traditional path of frequentist methodology. Trials using hypothesis tests of “no treatment effect” are done routinely, and the p-value < 0.05 is often the determinant of what constitutes a “successful” trial. Many drugs fail in clinical development, adding to the cost of new medicines, and some evidence points blame at the deficiencies of the frequentist paradigm. An unknown number effective medicines may have been abandoned because trials were declared “unsuccessful” due to a p-value exceeding 0.05. Recently, the Bayesian paradigm has shown utility in the clinical drug development process for its probability-based inference. We argue for a Bayesian approach that employs data from other trials as a “prior” for Phase 3 trials so that synthesized evidence across trials can be utilized to compute probability statements that are valuable for understanding the magnitude of treatment effect. Such a Bayesian paradigm provides a promising framework for improving statistical inference and regulatory decision making.     

Understanding Cumulative Risk Perception from Judgments and Choices: An Application to Flood Risks

Catastrophic events, such as floods, earthquakes, hurricanes, and tsunamis, are rare, yet the cumulative risk of each event occurring at least once over an extended time period can be substantial. In this work, we assess the perception of cumulative flood risks, how those perceptions affect the choice of insurance, and whether perceptions and choices are influenced by cumulative risk information. We find that participants' cumulative risk judgments are well represented by a bimodal distribution, with a group that severely underestimates the risk and a group that moderately overestimates it. Individuals who underestimate cumulative risks make more risk‐seeking choices compared to those who overestimate cumulative risks. Providing explicit cumulative risk information for relevant time periods, as opposed to annual probabilities, is an inexpensive and effective way to improve both the perception of cumulative risk and the choices people make to protect against that risk.     

Beyond tail median and conditional tail expectation: Extreme risk estimation using tail Lp-optimization

The conditional tail expectation (CTE) is an indicator of tail behavior that takes into account both the frequency and magnitude of a tail event. However, the asymptotic normality of its empirical estimator requires that the underlying distribution possess a finite variance; this can be a strong restriction in actuarial and financial applications. A valuable alternative is the median shortfall (MS), although it only gives information about the frequency of a tail event. We construct a class of tail L^p-medians encompassing the MS and CTE. For p in (1,2), a tail L^p-median depends on both the frequency and magnitude of tail events, and its empirical estimator is, within the range of the data, asymptotically normal under a condition weaker than a finite variance. We extrapolate this estimator and another technique to extreme levels using the heavy-tailed framework. The estimators are showcased on a simulation study and on real fire insurance data.     

相互保险的风险识别及创新解决方案——基于TRIZ和TIF理论

相互保险是保险组织形态中非常重要的一种,但是由于信息不对称,相对于其他保险模式而言,同样存在着逆向选择和道德风险问题。传统的监管模式下,监管渗透不够,反制力不强,导致了相互保险无法彻底解决逆向选择和道德风险的治理困境。本文基于塔福域理论和TRIZ理论系统地分析了相互保险模式中存在的风险,并且提出了创新性的解决方案,即构建“保险域”。     

对车险改革后保险营销的浅析

在车辆保险条款费率改革之后的车险市场上,现实状况却与预计效果相差甚远。其主要原因是,对保险营销战略的忽视,没有以相应的保险营销战略为指导,使得营销战术在操作过程中显得盲目而跟从。针对以上问题,我们首先要做的是树立正确的保险营销观念,即重新审视营销战略在车辆保险中的作用,并在此基础上建立广义的产品观念;同时注重服务在车险营销中的作用;有效地进行市场细分和市场选择;最后对车险营销战略的具体实施即营销战术提出建议。     

汽车保险改革后的市场现状分析

2003年我国实行车险费率改革,给我国汽车保险市场带来了巨大的变革。业务能力拓展、车险品种增多及费率市场化都是改革的成果。但同时,某些问题依然存在。文章在分析我国车险现状的基础上,指出了问题所在,并有针对性地提出了解决之道。     

Modelling daily multivariate pollutant data at multiple sites

Summary. This paper considers the spatiotemporal modelling of four pollutants measured daily at eight monitoring sites in London over a 4-year period. Such multiple-pollutant data sets measured over time at multiple sites within a region of interest are typical. Here, the modelling was carried out to provide the exposure for a study investigating the health effects of air pollution. Alternative objectives include the design problem of the positioning of a new monitoring site, or for regulatory purposes to determine whether environmental standards are being met. In general, analyses are hampered by missing data due, for example, to a particular pollutant not being measured at a site, a monitor being inactive by design (e.g. a 6-day monitoring schedule) or because of an unreliable or faulty monitor. Data of this type are modelled here within a dynamic linear modelling framework, in which the dependences across time, space and pollutants are exploited. Throughout the approach is Bayesian, with implementation via Markov chain Monte Carlo sampling.     

我国城镇养老保险存在的问题及对策探析

文章认为 ,我国城镇养老保险虽取得了很大的成绩 ,但还存在着诸多问题 ,作者对这些问题进行探讨和分析 ,并提出了切实可行的解决对策     

Computing maximum likelihood estimates from type II doubly censored exponential data

It is well-known that, under Type II double censoring, the maximum likelihood (ML) estimators of the location and scale parameters, θ and δ, of a twoparameter exponential distribution are linear functions of the order statistics. In contrast, when θ is known, theML estimator of δ does not admit a closed form expression. It is shown, however, that theML estimator of the scale parameter exists and is unique. Moreover, it has good large-sample properties. In addition, sharp lower and upper bounds for this estimator are provided, which can serve as starting points for iterative interpolation methods such as regula falsi. Explicit expressions for the expected Fisher information and Cramér-Rao lower bound are also derived. In the Bayesian context, assuming an inverted gamma prior on δ, the uniqueness, boundedness and asymptotics of the highest posterior density estimator of δ can be deduced in a similar way. Finally, an illustrative example is included.