cumulative distribution

简明释义

累积分布

英英释义

例句

1.The cumulative distribution can be plotted to visualize the data more effectively.

可以绘制累积分布以更有效地可视化数据。

2.We used the cumulative distribution to analyze the test scores of students.

我们使用累积分布来分析学生的考试成绩。

3.In statistics, the cumulative distribution is crucial for determining percentiles.

在统计学中，累积分布对于确定百分位数至关重要。

4.The cumulative distribution function helps us understand the probability of a variable being less than or equal to a certain value.

这个累积分布函数帮助我们理解一个变量小于或等于某个值的概率。

5.Understanding the cumulative distribution of income can provide insights into economic inequality.

理解收入的累积分布可以提供对经济不平等的洞察。

作文

In the field of statistics, understanding various concepts is crucial for analyzing data effectively. One such concept is the cumulative distribution, which plays a significant role in probability theory and statistics. The cumulative distribution function (CDF) is a fundamental tool that helps us understand the likelihood of a random variable taking on a value less than or equal to a certain threshold. In simpler terms, it provides a way to visualize the distribution of probabilities across different values of a variable.To grasp the importance of the cumulative distribution, let’s consider an example involving test scores. Imagine a class of students who took a math exam. If we were to plot the individual scores on a graph, we would see how many students scored at each particular level. However, this raw data does not provide a complete picture. By utilizing the cumulative distribution function, we can create a new graph that shows the percentage of students who scored below a certain score. For instance, if we want to know how many students scored less than 70%, the CDF will allow us to see this information clearly.The cumulative distribution function is particularly useful because it allows for easy comparisons between different datasets. For example, if we have two classes that took the same exam, we can use their respective CDFs to compare their performance. This comparison can reveal insights that raw scores alone cannot. We might find that while one class had a higher average score, the other class had a lower number of students scoring poorly. This nuanced understanding is vital in educational assessments and can help educators identify areas needing improvement.Moreover, the cumulative distribution is not limited to educational contexts; it is widely applicable in various fields, including finance, engineering, and social sciences. In finance, investors often analyze the cumulative distribution of returns on investment to assess risk. By examining the CDF of historical stock prices, investors can determine the probability of achieving a certain return, which aids in making informed decisions about where to allocate resources.In engineering, reliability analysis often employs the cumulative distribution to predict the lifespan of products. By understanding the probability of failure over time, engineers can design more reliable systems and anticipate maintenance needs. Similarly, in social sciences, researchers may use the cumulative distribution to examine income distribution within a population, helping policymakers understand economic disparities.One of the key features of the cumulative distribution function is that it is always non-decreasing. This means that as you move along the x-axis (the variable axis), the values of the CDF never decrease. This property reflects the cumulative nature of the function: as you consider more values, the total probability either remains the same or increases. Additionally, the CDF approaches 1 as the variable approaches infinity, indicating that the total probability of all possible outcomes is 100%.In conclusion, the cumulative distribution function is an essential concept in statistics that provides valuable insights into data analysis. Whether in education, finance, engineering, or social sciences, understanding the CDF allows for better decision-making and a deeper comprehension of underlying patterns in data. By employing the cumulative distribution, we can transform raw data into meaningful information, paving the way for informed conclusions and actions based on statistical evidence.

在统计学领域，理解各种概念对有效分析数据至关重要。其中一个概念是累积分布，它在概率论和统计学中起着重要作用。累积分布函数（CDF）是一种基本工具，帮助我们理解随机变量取值小于或等于某个阈值的可能性。简单来说，它提供了一种可视化不同变量值的概率分布的方法。为了理解累积分布的重要性，我们可以考虑一个涉及测试分数的例子。想象一下，一班学生参加了数学考试。如果我们在图表上绘制每个学生的单独分数，我们将看到有多少学生在每个特定水平上得分。然而，这些原始数据并没有提供完整的画面。通过利用累积分布函数，我们可以创建一张新图，显示得分低于某个分数的学生百分比。例如，如果我们想知道有多少学生得分低于70%，CDF将清晰地显示这些信息。累积分布函数特别有用，因为它允许轻松比较不同的数据集。例如，如果我们有两个班级参加同一考试，我们可以使用它们各自的CDF来比较它们的表现。这种比较可以揭示仅靠原始分数无法看出的见解。我们可能会发现，尽管一个班级的平均分较高，但另一个班级的低分学生数量较少。这种细致的理解在教育评估中至关重要，可以帮助教育工作者识别需要改进的领域。此外，累积分布不仅限于教育背景；它在金融、工程和社会科学等各个领域广泛适用。在金融领域，投资者常常分析投资回报的累积分布以评估风险。通过检查历史股价的CDF，投资者可以确定实现某种回报的概率，从而帮助做出明智的资源分配决策。在工程领域，可靠性分析通常利用累积分布来预测产品的生命周期。通过理解随时间推移的故障概率，工程师可以设计更可靠的系统并预期维护需求。类似地，在社会科学中，研究人员可能使用累积分布来考察人口中的收入分配，帮助政策制定者理解经济差距。累积分布函数的一个关键特征是它总是非递减的。这意味着当你沿着x轴（变量轴）移动时，CDF的值永远不会减少。这一特性反映了函数的累积性质：当你考虑更多的值时，总概率要么保持不变，要么增加。此外，CDF在变量接近无穷大时趋近于1，表明所有可能结果的总概率为100%。总之，累积分布函数是统计学中的一个基本概念，为数据分析提供了宝贵的见解。无论是在教育、金融、工程还是社会科学中，理解CDF都能促进更好的决策和对数据中潜在模式的更深理解。通过使用累积分布，我们可以将原始数据转化为有意义的信息，为基于统计证据的明智结论和行动铺平道路。