marginal distribution

简明释义

边际分配

英英释义

例句

1.The marginal distribution 边际分布 of survey responses can reveal patterns that are not immediately obvious.

调查回应的边际分布可以揭示一些不易察觉的模式。

2.The marginal distribution 边际分布 of income levels helps us understand economic disparities in the population.

收入水平的边际分布有助于我们理解人口中的经济差异。

3.To visualize the data, we plotted the marginal distribution 边际分布 of age and income on separate axes.

为了可视化数据，我们在不同的坐标轴上绘制了年龄和收入的边际分布。

4.In a study of student performance, we analyzed the marginal distribution 边际分布 of grades across different subjects.

在一项学生表现的研究中，我们分析了不同科目成绩的边际分布。

5.By examining the marginal distribution 边际分布 of two variables, we can identify potential correlations.

通过检查两个变量的边际分布，我们可以识别潜在的相关性。

作文

In the field of statistics, understanding various concepts is crucial for analyzing data effectively. One such concept is marginal distribution, which plays a significant role in probability theory and statistical inference. The term marginal distribution refers to the probability distribution of a subset of variables within a larger set, obtained by summing or integrating over the other variables. This concept helps statisticians and researchers to focus on specific variables while still considering the influence of others. To illustrate the importance of marginal distribution, let’s consider a practical example involving a survey conducted to understand the relationship between education level and income. In this survey, we collect data on individuals' education levels (such as high school, bachelor’s, and master’s degrees) and their corresponding incomes. The joint distribution of these two variables can be complex, but by calculating the marginal distribution of income, we can gain insights into the overall income levels across different educational backgrounds.The marginal distribution of income can be computed by summing the incomes for each education level. For instance, if we find that individuals with a bachelor’s degree earn an average of $60,000, those with a master’s degree earn $80,000, and high school graduates earn $40,000, we can create a marginal distribution table that summarizes these findings. This table allows us to see the overall distribution of income without getting lost in the complexities of the joint distribution.Moreover, the marginal distribution provides valuable information for decision-making. For policymakers and educators, understanding how income varies with education can guide initiatives aimed at improving educational access and economic opportunities. By focusing on the marginal distribution of income, they can identify trends and disparities that require attention.Another important aspect of marginal distribution is its application in Bayesian statistics. In Bayesian analysis, we often deal with multiple parameters, and the marginal distribution helps in deriving the distribution of one parameter while integrating out the others. This approach is essential for making predictions and updating beliefs based on new data. For instance, if we are interested in predicting future income levels based on education, we can use the marginal distribution to simplify our calculations and focus on the relevant factors.In conclusion, mastering the concept of marginal distribution is vital for anyone working with statistical data. It not only simplifies complex relationships among variables but also enhances our understanding of the underlying patterns. Whether in academic research, policy formulation, or business analytics, the ability to compute and interpret marginal distribution is an invaluable skill. As we continue to collect and analyze data in various fields, the significance of marginal distribution will only grow, enabling us to make more informed decisions based on statistical evidence.

在统计学领域，理解各种概念对于有效分析数据至关重要。其中一个重要概念是边际分布，它在概率论和统计推断中发挥着重要作用。术语边际分布指的是在更大集合中某个子集变量的概率分布，通过对其他变量进行求和或积分得到。这个概念帮助统计学家和研究人员专注于特定变量，同时考虑其他变量的影响。为了说明边际分布的重要性，让我们考虑一个关于教育水平与收入关系的调查的实际例子。在这项调查中，我们收集了个人的教育水平（如高中、本科和硕士学位）及其相应的收入数据。这两个变量的联合分布可能很复杂，但通过计算收入的边际分布，我们可以获得不同教育背景下整体收入水平的见解。收入的边际分布可以通过对每个教育水平的收入进行求和来计算。例如，如果我们发现本科毕业生的平均收入为60,000美元，硕士毕业生为80,000美元，高中毕业生为40,000美元，我们可以创建一个总结这些发现的边际分布表。这个表让我们能够看到整体收入的分布，而不会迷失在联合分布的复杂性中。此外，边际分布为决策提供了宝贵的信息。对于政策制定者和教育工作者来说，理解收入如何随教育而变化可以指导改善教育机会和经济机会的倡议。通过关注收入的边际分布，他们可以识别出需要关注的趋势和差距。边际分布的另一个重要方面是它在贝叶斯统计中的应用。在贝叶斯分析中，我们通常处理多个参数，而边际分布有助于在整合其他参数的同时推导一个参数的分布。这种方法对于基于新数据进行预测和更新信念至关重要。例如，如果我们希望根据教育水平预测未来的收入水平，我们可以使用边际分布来简化我们的计算，专注于相关因素。总之，掌握边际分布的概念对于任何处理统计数据的人来说都是至关重要的。它不仅简化了变量之间的复杂关系，还增强了我们对潜在模式的理解。无论是在学术研究、政策制定还是商业分析中，计算和解释边际分布的能力都是一项宝贵的技能。随着我们在各个领域继续收集和分析数据，边际分布的重要性只会增加，使我们能够基于统计证据做出更明智的决策。