truncated distribution

简明释义

截尾分布

英英释义

例句

1.When dealing with test scores, a truncated distribution 截断分布 may arise if only students who passed are included in the analysis.

在处理考试分数时，如果分析中仅包括通过的学生，则可能出现 truncated distribution 截断分布。

2.The finance department reported that the returns on investment followed a truncated distribution 截断分布 due to the exclusion of negative returns.

财务部门报告称，由于排除了负收益，投资回报遵循 truncated distribution 截断分布。

3.Researchers used a truncated distribution 截断分布 model to better fit the observed data from the experiment.

研究人员使用 truncated distribution 截断分布 模型来更好地拟合实验中观察到的数据。

4.In statistics, a truncated distribution 截断分布 occurs when values above or below a certain threshold are not considered.

在统计学中，truncated distribution 截断分布 是指超出某个阈值的值不被考虑的情况。

5.The analysis of income data often assumes a truncated distribution 截断分布 since extremely high incomes are frequently excluded.

收入数据的分析通常假设存在 truncated distribution 截断分布，因为极高的收入常常被排除在外。

作文

In the field of statistics, understanding various types of distributions is crucial for data analysis and interpretation. One such concept is the truncated distribution, which refers to a probability distribution that has been limited or 'truncated' at certain values. This means that values below or above a specified threshold are not considered in the analysis, leading to a modified distribution that reflects only a subset of the entire population. The truncated distribution is particularly useful in scenarios where extreme values may skew the results or when focusing on a specific range of interest.For instance, consider a scenario in which a researcher is studying the heights of adult males in a specific city. If the researcher decides to exclude individuals shorter than 150 cm and taller than 200 cm from the analysis, the resulting data set would represent a truncated distribution. This approach allows the researcher to concentrate on a more relevant segment of the population, which can yield more meaningful insights.The mathematical formulation of a truncated distribution involves adjusting the probability density function (PDF) to account for the truncated values. In essence, the PDF is re-normalized so that the total area under the curve remains equal to one, despite the exclusion of certain values. This ensures that the probabilities of the remaining values reflect their true likelihood within the specified bounds.Moreover, the truncated distribution can arise in various practical situations. For instance, in insurance, companies often deal with claims that exceed a certain amount. By analyzing only those claims that fall within a specific range, insurers can better understand risk and set premiums accordingly. Similarly, in economics, researchers might focus on income levels above a certain threshold to study wealth distribution among the affluent, thus employing a truncated distribution to gain insights into this demographic.It is also important to distinguish between truncated distributions and censored distributions. While both concepts involve limiting data, they differ fundamentally. A truncated distribution excludes certain values outright, whereas a censored distribution includes all values but only partially observes them. For example, if a study on income reports that individuals earning above a certain amount are simply noted as 'above threshold', this represents a censored distribution rather than a truncated one.Understanding the implications of using a truncated distribution is essential for accurate data interpretation. It is vital to recognize how truncation affects statistical measures such as mean, variance, and standard deviation. For instance, the mean of a truncated distribution may be significantly higher than that of the original distribution due to the exclusion of lower values. Thus, analysts must exercise caution and transparency when presenting findings based on truncated data.In conclusion, the truncated distribution is a powerful statistical tool that allows researchers and analysts to focus on specific segments of data while excluding unwanted extremes. Its applications span various fields, including social sciences, economics, and insurance. However, it is imperative to understand the underlying mechanics and implications of using a truncated distribution to ensure accurate conclusions and informed decision-making. As we continue to navigate an increasingly data-driven world, mastering concepts like the truncated distribution will undoubtedly enhance our analytical capabilities and contribute to more robust research outcomes.

在统计学领域，理解各种类型的分布对于数据分析和解释至关重要。其中一个概念是截断分布，它指的是在某些值上被限制或“截断”的概率分布。这意味着在分析中不考虑低于或高于特定阈值的值，从而导致一个只反映整个总体子集的修改后的分布。截断分布在极端值可能扭曲结果或专注于特定感兴趣范围的场景中尤其有用。例如，考虑一个研究者在特定城市研究成年男性身高的场景。如果研究者决定排除身高低于150厘米和高于200厘米的个体，则得到的数据集将代表一个截断分布。这种方法使研究者能够集中关注更相关的人群，从而产生更有意义的见解。截断分布的数学公式涉及调整概率密度函数（PDF），以考虑截断值。实质上，PDF被重新归一化，以确保尽管排除了某些值，但曲线下的总面积仍然等于1。这确保了剩余值的概率反映了在指定范围内的真实可能性。此外，截断分布可以在各种实际情况下出现。例如，在保险行业，公司通常处理超过某一金额的索赔。通过分析仅在特定范围内的索赔，保险公司可以更好地理解风险并相应地设定保费。同样，在经济学中，研究人员可能会专注于高于某一阈值的收入水平，以研究富裕人群的财富分布，从而采用截断分布来深入了解这一人群。还需要区分截断分布和审查分布。虽然这两个概念都涉及限制数据，但它们在根本上是不同的。截断分布完全排除某些值，而审查分布则包括所有值，但仅部分观察它们。例如，如果一项关于收入的研究报告显示，收入超过某一金额的个体仅被标记为“超过阈值”，这就代表了一个审查分布，而不是截断分布。理解使用截断分布的影响对于准确的数据解释至关重要。必须认识到截断如何影响诸如均值、方差和标准差等统计测量。例如，截断分布的均值可能因排除了较低值而显著高于原始分布的均值。因此，分析师在呈现基于截断数据的发现时，必须谨慎和透明。总之，截断分布是一个强大的统计工具，使研究人员和分析师能够专注于特定的数据段，同时排除不需要的极端值。它的应用遍及社会科学、经济学和保险等多个领域。然而，理解使用截断分布的基本机制和影响对于确保准确的结论和明智的决策至关重要。随着我们继续在一个日益数据驱动的世界中航行，掌握像截断分布这样的概念无疑会增强我们的分析能力，并有助于更稳健的研究结果。