Underprotection of Unpredictable Statistical Lives Compared to Predictable Ones

Existing ethical discussion considers the differences in care for identified versus statistical lives. However, there has been little attention to the different degrees of care that are taken for different kinds of statistical lives. Here we argue that for a given number of statistical lives at stake, there will sometimes be different, and usually greater, care taken to protect predictable statistical lives, in which the number of lives that will be lost can be predicted fairly accurately, than for unpredictable statistical lives, where the lives are at stake because of a low‐probability event, such that most likely no one will be affected by the decision but with low probability some lives will be at stake. One reason for this difference is the statistical challenge of estimating low probabilities, and in particular the tendency of common approaches to underestimate these probabilities. Another is the existence of rational incentives to treat unpredictable risks as if the probabilities were lower than they are. Some of these factors apply outside the pure economic context, to institutions, individuals, and governments. We argue that there is no ethical reason to treat unpredictable statistical lives differently from predictable statistical lives. Moreover, lives that are unpredictable from the perspective of an individual agent may become predictable when aggregated to the level of a societal decision. Underprotection of unpredictable statistical lives is a form of market failure that may need to be corrected by altering regulation, introducing compulsory liability insurance, or other social policies.     

关于财务软件中商品单价出现负数问题的分析与对策

使用财务软件核算存货时，存货单价及数量会出现负数，可运用三种方法解决：重新建账法、追溯调整法、逐个调整法。使存货金额反映出企业真实数据。     

Estimation and selection procedures in regression: An L1 approach

The authors consider the problem of estimating a regression function go involving several variables by the closest functional element of a prescribed class _G that is closest to it in the L₁ norm. They propose a new estimator ? based on independent observations and give explicit finite sample bounds for the L₁distance between ?g and go. They apply their estimation procedure to the problem of selecting the smoothing parameter in nonparametric regression.     

《醒世姻缘传》概数表示法研究

概数表示法对于语言表达的准确性和生动性具有重要的意义。产生于明末清初的通俗小说《醒世姻缘传》中的概数表示法种类多样，体现出山东方言中的一些特殊用法，反映了山东方言称数法由近代汉语向现代汉语过渡的特点。     

Prior distributions for variance parameters in a sparse-event meta-analysis of a few small trials

In rare diseases, typically only a small number of patients are available for a randomized clinical trial. Nevertheless, it is not uncommon that more than one study is performed to evaluate a (new) treatment. Scarcity of available evidence makes it particularly valuable to pool the data in a meta-analysis. When the primary outcome is binary, the small sample sizes increase the chance of observing zero events. The frequentist random-effects model is known to induce bias and to result in improper interval estimation of the overall treatment effect in a meta-analysis with zero events. Bayesian hierarchical modeling could be a promising alternative. Bayesian models are known for being sensitive to the choice of prior distributions for between-study variance (heterogeneity) in sparse settings. In a rare disease setting, only limited data will be available to base the prior on, therefore, robustness of estimation is desirable. We performed an extensive and diverse simulation study, aiming to provide practitioners with advice on the choice of a sufficiently robust prior distribution shape for the heterogeneity parameter. Our results show that priors that place some concentrated mass on small τ values but do not restrict the density for example, the Uniform(−10, 10) heterogeneity prior on the log(τ²) scale, show robust 95% coverage combined with less overestimation of the overall treatment effect, across varying degrees of heterogeneity. We illustrate the results with meta-analyzes of a few small trials.     

Generating autocorrelated pseudo-random numbers with specific distributions

An easily implemented and computationally efficient procedure is presented for the generation of autocorrelated pseudo-random numbers with specific probability distributions. A plot illustrates the relationship among the autocorrelations of the uniform, Rayleigh, and exponential distributions corresponding to a given autocorrelation in the normal generating distribution.     

The negative contagion reflection of the polya-eggenberger distribution

The Polya-Eggenberger distribution Involves drawing a ball from an urn containing black and white balls and, after each drawing, returning the ball together with s balls of the same color, The model represents positive contagion since the added balls are the same color as the one drawn, See Johnson and Kotz, (1977),

This paper derives and examines the probability distribution which results from the Polya-Eggenberger model with only one change namely, the s additional balls added after each drawing are of the opposite color, producing a negative contagion model.

Formulas in closed form are presented for the probability distribution function, the mean and variance, all binomial moments and, where s is greater than or equal to the number of balls in the urn at start, the mode, A formula for the mode is conjectured where s is less than the number of balls in the urn at start.

Finally, the probability of obtaining k black balls in n drawings is shown in certain instances to be equal to A_nk/n!

where A_nk are the Eulerian numbers.     

Recurrence relations for the minimum variance unbiased estimator of the probability function of the R distribution

We obtain a new technique to calculate the value of the minimum variance unbiased estimator (MVUE) of the probability function (p.f.) of the R distribution. This technique is based on an investigation of the ratios of r numbers. A recurrence relation for the MVUE of the p.f. of the R distribution is derived. It is interesting that the derived relation does not depend on the r numbers but depends on the ratios of the r numbers. The new method is efficient, convenient and accurate.     

Extended stirling family of discrete probability distributions

In this paper. introduced is a family of discrete probability distributions. whose probability function includes explieitly the Striling-Carlitz polynomial of the first or the second kind. The new family extends the stirling family of distributions. Sibuya (1988) includes the conditional distributions of the orginal ones and enlarges the application area.