marginal distribution

简明释义

边缘分布

英英释义

例句

1.The marginal distribution 边际分布 of exam scores provides insight into overall student performance.

考试成绩的边际分布 边际分布提供了对整体学生表现的洞察。

2.By examining the marginal distribution 边际分布 of heights, we can see the variation among different age groups.

通过检查身高的边际分布 边际分布，我们可以看到不同年龄组之间的差异。

3.In a two-way table, the marginal distribution 边际分布 of variable A shows the total counts for each category of A.

在一个双向表中，变量A的边际分布 边际分布显示了每个类别的总计数。

4.To understand the relationship between age and income, we can analyze the marginal distribution 边际分布 of each variable separately.

为了理解年龄和收入之间的关系，我们可以分别分析每个变量的边际分布 边际分布。

5.The marginal distribution 边际分布 of a dataset helps in identifying the frequency of individual categories.

数据集的边际分布 边际分布有助于识别各个类别的频率。

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 statistics. The marginal distribution refers to the probability distribution of a subset of variables within a larger set, while ignoring the other variables. This means that it provides insights into the behavior of one or more variables without considering the influence of others. For instance, if we have a dataset containing information about students' grades in mathematics and science, the marginal distribution of mathematics grades would show how those grades are distributed independently of science grades.The importance of marginal distribution lies in its ability to simplify complex datasets. When dealing with multivariate data, it can be overwhelming to analyze all variables simultaneously. By focusing on the marginal distribution, researchers can isolate specific variables and examine their individual characteristics. This simplification allows for a clearer understanding of trends and patterns that may not be apparent when considering the entire dataset.Moreover, the marginal distribution can be calculated by summing or integrating the joint distribution over the other variables. For example, if we have a joint probability distribution of two random variables, X and Y, the marginal distribution of X can be found by summing the probabilities of all possible values of Y. This process highlights how one variable behaves on its own, independent of the other variable's influence.In practical applications, marginal distribution is widely used in various fields such as economics, psychology, and health sciences. For instance, in an economic study examining consumer behavior, researchers may want to analyze the marginal distribution of income levels to understand spending habits. By looking at income distribution alone, they can identify trends and make informed decisions without the noise created by other factors like age or education level.Furthermore, the marginal distribution is essential for making predictions. In machine learning and statistical modeling, understanding the marginal distribution of input features can help in building more accurate models. By recognizing how each feature behaves independently, data scientists can create algorithms that account for these individual distributions, leading to better predictions and insights.In conclusion, the concept of marginal distribution is vital for anyone working with statistical data. It allows researchers to focus on specific variables, simplifies complex datasets, and aids in making predictions. By understanding the marginal distribution, one can gain valuable insights that contribute to more effective data analysis and decision-making processes. As data continues to grow in complexity, mastering such concepts will become increasingly important for researchers and practitioners alike.

在统计学领域，理解各种概念对于有效分析数据至关重要。其中一个重要的概念是边际分布，它在概率论和统计学中发挥着重要作用。边际分布指的是在忽略其他变量的情况下，较大集合中某一子集变量的概率分布。这意味着它提供了关于一个或多个变量行为的见解，而不考虑其他变量的影响。例如，如果我们有一个包含学生数学和科学成绩的信息数据集，那么数学成绩的边际分布将显示这些成绩在独立于科学成绩的情况下是如何分布的。边际分布的重要性在于它能够简化复杂的数据集。在处理多变量数据时，同时分析所有变量可能会令人感到不知所措。通过关注边际分布，研究人员可以孤立特定变量，并检查它们各自的特征。这种简化使得对趋势和模式的理解更加清晰，这些趋势和模式在考虑整个数据集时可能并不明显。此外，边际分布可以通过对其他变量的联合分布进行求和或积分来计算。例如，如果我们有两个随机变量X和Y的联合概率分布，可以通过对Y的所有可能值的概率求和来找到X的边际分布。这个过程突显了一个变量在没有其他变量影响的情况下的行为。在实际应用中，边际分布在经济学、心理学和健康科学等多个领域被广泛使用。例如，在一项经济研究中，研究人员可能希望分析收入水平的边际分布以了解消费习惯。通过仅查看收入分布，他们可以识别趋势并做出明智的决策，而不受年龄或教育水平等其他因素的干扰。此外，边际分布对于预测至关重要。在机器学习和统计建模中，理解输入特征的边际分布可以帮助构建更准确的模型。通过认识到每个特征独立的行为，数据科学家可以创建考虑这些个体分布的算法，从而导致更好的预测和见解。总之，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。它允许研究人员专注于特定变量，简化复杂数据集，并有助于做出预测。通过理解边际分布，人们可以获得有价值的见解，从而有助于更有效的数据分析和决策过程。随着数据复杂性的不断增加，掌握这样的概念对于研究人员和从业者来说将变得越来越重要。