cumulative distribution

简明释义

累积数分布

英英释义

例句

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

这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。

2.In statistics, the cumulative distribution is often used to summarize data sets.

在统计学中，累积分布通常用于总结数据集。

3.The cumulative distribution of test scores indicates how many students scored below a certain threshold.

测试分数的累积分布表明有多少学生的分数低于某个阈值。

4.To visualize the data, we can plot the cumulative distribution against the values.

为了可视化数据，我们可以将累积分布与数值进行绘图。

5.By examining the cumulative distribution, we can identify the median of the data.

通过检查累积分布，我们可以确定数据的中位数。

作文

In statistics, understanding the concept of cumulative distribution is crucial for analyzing data sets and interpreting probability distributions. The term refers to a function that describes the probability that a random variable takes on a value less than or equal to a specific value. This function is essential in various fields such as economics, engineering, and social sciences, where it helps researchers and analysts make informed decisions based on data analysis.To illustrate the importance of cumulative distribution, let’s consider an example involving test scores. Suppose we have a group of students who took a standardized test, and we want to analyze their performance. By calculating the cumulative distribution of the test scores, we can determine the percentage of students who scored below a certain threshold. For instance, if the cumulative distribution at a score of 75 indicates that 80% of students scored below this mark, we can conclude that a significant majority performed well.The cumulative distribution function (CDF) is particularly useful because it provides a complete picture of the distribution of values within our dataset. Unlike the probability density function (PDF), which only gives us the likelihood of a particular outcome, the CDF allows us to understand the accumulation of probabilities up to a given point. This characteristic makes it an invaluable tool for researchers who need to assess risks or probabilities in various scenarios.Furthermore, the cumulative distribution can be applied to various types of data, including continuous and discrete variables. For continuous variables, the CDF is a smooth curve that increases from zero to one, while for discrete variables, it appears as a step function. Regardless of the type of data, the cumulative distribution provides insights into the overall behavior of the dataset, allowing for better predictions and analyses.In addition to its practical applications, the cumulative distribution is also foundational in theoretical statistics. It plays a critical role in hypothesis testing, confidence interval estimation, and many other statistical methodologies. By understanding how to calculate and interpret the cumulative distribution, statisticians can derive meaningful conclusions from their analyses.Moreover, the cumulative distribution can be used in conjunction with other statistical tools and concepts. For example, when analyzing the relationship between two variables, researchers may use the joint cumulative distribution to explore how the probabilities of outcomes change based on the interaction of those variables. This multidimensional approach enhances the depth of statistical analysis and allows for more nuanced interpretations of data.In conclusion, the concept of cumulative distribution is a fundamental aspect of statistics that aids in the understanding and interpretation of data. It provides valuable insights into the probabilities associated with random variables and is applicable across various fields. By mastering the use of cumulative distribution, researchers and analysts can enhance their ability to make data-driven decisions, ultimately leading to more accurate conclusions and better outcomes in their respective domains.

在统计学中，理解累积分布的概念对于分析数据集和解释概率分布至关重要。该术语指的是一个函数，它描述了随机变量取值小于或等于特定值的概率。这个函数在经济学、工程学和社会科学等多个领域中都是必不可少的，它帮助研究人员和分析师根据数据分析做出明智的决策。为了说明累积分布的重要性，让我们考虑一个关于考试成绩的例子。假设我们有一组学生参加了标准化考试，我们想要分析他们的表现。通过计算考试成绩的累积分布，我们可以确定有多少百分比的学生在某个阈值以下得分。例如，如果在75分的累积分布中显示80%的学生得分低于这个分数，那么我们可以得出大多数学生表现良好的结论。累积分布函数（CDF）尤其有用，因为它提供了我们数据集中值分布的完整图景。与只给出特定结果可能性的概率密度函数（PDF）不同，CDF使我们能够理解到达某一点为止的概率积累。这一特性使其成为研究人员评估各种情境中的风险或概率的宝贵工具。此外，累积分布可以应用于各种类型的数据，包括连续变量和离散变量。对于连续变量，CDF是从零到一平滑上升的曲线，而对于离散变量，它则呈现为阶梯函数。无论数据类型如何，累积分布都提供了对数据集整体行为的洞察，从而允许更好的预测和分析。除了其实际应用外，累积分布在理论统计学中也是基础。它在假设检验、置信区间估计以及许多其他统计方法中发挥着关键作用。通过了解如何计算和解释累积分布，统计学家可以从分析中得出有意义的结论。此外，累积分布还可以与其他统计工具和概念结合使用。例如，在分析两个变量之间的关系时，研究人员可以使用联合累积分布来探索这些变量交互作用下结果的概率如何变化。这种多维方法增强了统计分析的深度，使数据的解释更加细致。总之，累积分布的概念是统计学的一个基本方面，有助于理解和解释数据。它提供了与随机变量相关的概率的宝贵见解，并适用于各个领域。通过掌握累积分布的使用，研究人员和分析师可以提高他们基于数据做出决策的能力，从而最终导致更准确的结论和更好的结果。