置信区间

Meanwhile, it could be seen that there does not exist a confidence interval with width less than 0.5 because of the property of Poisson distribution. Based on these conditions, the author mainly carried out research into two aspects of this problem as follows. Firstly, by numerical and theoretical analysis, the author compares some existent confidence intervals, for example,"exact" confidence interval, Wald confidence interval and Bayesian confidence interval, and finds some deficiencies points of the confidence intervals, whose modification version has been proposed .Also, several better confidence intervals such asare also presented .Secondly, for given confidence coefficient and interval width, the author constructs a class of asymptotical two-stage interval estimate procedures. At the same time, under varies restriction of confidence coefflcientent interval width, the optional sample size of the first stage has been computed by numerical computation. The numerical computation shows that the method considered in this dissertation have good properties and applied value.

同时，由于Poisson分布的特性，我们知道不存在其参数区间长度小于0.5的置信区间，基于这些情况，我们主要展开了以下两个方面的研究：一是利用数值计算分析与理论分析的方法对现有的若干置信区间如"精确"置信区间，Wald置信区间，Bayes置信区间等进行分析比较，发现了一些缺陷，针对这些缺陷，我们进行适当的修正，并得到几种性质较好的置信区间如：修正大样本区间Jeffreys原则下置信区间二是针对已给定的置信系数与区间长度，我们提出了一种渐近的两阶段区间估计程序，并利用数值计算的方法，在各种置信系数与区间长度限定下，算出了最优的第一阶段观测次数，大量数据表明，本文考虑的方法性态良好，具有应用价值。

The the probabilistic forecasting method of the error between the sample mean and expectation value of the random variable utilizing the central limit theory was researched, then the mathematical formula for the relation between sampling size and variance coefficient of loss of load probability was analyzed. Furthermore, the formulas for the relation between confidence intervals of variance coefficient and sampling size are deduced.

基于中心极限定理深入研究随机变量的样本均值与期望值之间误差的概率预测方法，在此基础上分析失负荷概率(loss of load probability，LOLP)指标的方差系数和样本容量之间的关系表达式，导出方差系数给定时的样本容量置信区间公式及样本容量给定时的方差系数置信区间公式。

According to the LC-P line of each of insecticide in the mixture and the formula of co-toxicity factor, several expected mortality and the region of additive action (expected mortality±20% expected mortality) were calculated, and according to observed mortality of mixture, the 95% confidence interval was calculated, LC-P line of expected mortality with the region of additive action and LC-P line of observed mortality with the 95% confidence interval were drawn, it was found that there was overlap between the region of additive action and 95% confidence interval and two lines crossed each other when co-toxicity coefficient was more than 100 and the co-toxicity factor was less than 20, which meant there was no significant differences between expected mortality and observed mortality, and that there was on or a few overlap between the region of additive action and 95% confidence interval when co-toxicity coefficient was more than 100 and the co-toxicity factor was more than 20 or co-toxicity coefficient was less than 100 and the co-toxicity factor was less than 20, which meant there was significant differences between expected mortality and observed mortality.

根据单剂的LC-P线和共毒因子公式，求出混剂的期望死亡率和"相加作用区间"（期望死亡率±20%期望死亡率），根据混剂的实测死亡率求出95%置信区间，画出期望LC-P线及"相加作用区间"和实测LC-P线及"95%置信区间"，发现当共毒系数大于100、共毒因子小于20时，实测LC-P线和期望LC-P线彼此交缠，期望LC-P线的"相加作用区间"和实测LC-P线的"95%置信区间"能高度重叠，表明两条LC-P线之间没有毒力差异；当共毒系数大于100、共毒因子大于20，或者共毒系数小于100、共毒因子小于-20时，实测LC-P线的"95%置信区间"和期望LC-P线的"相加作用区间"只有少量重叠或完全不重叠，体现出了实测LC-P线和期望LC-P线对供试害虫的毒力差异。

The confidence interval of unknown parameter represents the range of the value and the reliability about estimation of parameter.

未知参数的置信区间表示该参数的取值范围及其可信程度，置信区间的长度表示区间估计的精度。

We estimated that in 2005, a total of 673,000 deaths (95% confidence interval , 564,700 to 781,400) were attributable to smoking in China: 538,200 (95% CI, 455,800 to 620,600) among men and 134,800 (95% CI, 108,900 to 160,800) among women.

根据我们的估算，2005年中，中国共有673000例死亡人数是由吸烟引起的（置信区间95%，564700到781400），其中男性538200例（置信区间95%，455800到620600），女性134800例（置信区间95%，108900到160800）。

Results The ED50 for isobaric bupivacaine was 8.0 mg, 95% CI 7.1 mg to 9.0 mg.

结果 布比卡因的ED50为8.0 mg(95%置信区间为7.1～9.0 mg)，ED95为11.3 mg(95%置信区间为9.7～21.4 mg)。

Firstly, we discuss several two-sided confidence intervals of binominal distribution such as: the Standard interval, the Wilson interval, the Agresti-Coull interval, Jeffreys interval, and do some comparative analysis among them, mainly consider the average converage probability and the average expected length of the co...

我们先介绍了二项分布参数的几种双侧置信区间：标准区间、Wilso区间、Agresti-Coull区间和Jeffreys区间，并对它们进行了比较分析，主要从置信区间的平均覆盖率和置信区间的期望长度来考虑。

In unusual cases, a confidence set may consist of a collection of several separate intervals, which may include semi-infinite intervals, and it is possible that an outcome of a confidence-interval calculation could be the set of all values from minus infinity to plus infinity.

在个别情况下，一个置信系列可以由一系列的多个单独区间组成，其中可能包括半无穷区间。这种情况下，一个置信区间的结果值有可能会是这一系列值当中的一个。

For a given proportion p (where p is the confidence level), a confidence interval for a population parameter is an interval that is calculated from a random sample of an underlying population such that, if the sampling was repeated numerous times and the confidence interval recalculated from each sample according to the same method, a proportion p of the confidence intervals would contain the population parameter in question.

对于一个比例 P而言，一个群体参数的置信区间中的区间是由一个基础群体的随意样本计算出的，假如样本被重复了无数次，置信区间也根据每个样本，以同样的方法重新计算，那么这个置信区间中的比例 P 将要重新定论。

Assume β=1, and confidence level is 0.95, the length of normal confidence interval is compared to the length of shortest confidence interval, the results show: both absolute difference d and relative difference e are decreased by the increasing sample number n, when n≤9, e≥10%.

在假设参数β=1，置信水平为0.95的条件下，比较了常用置信区间与最短置信区间的长度，结果表明：两者长度的绝对差d和相对差e均随样本容量n的增大而减小，当n≤9时，e≥10%。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。