central moment

简明释义

中心力矩

英英释义

例句

1.The first central moment 中心矩 is always zero, representing the mean of the distribution.

第一个中心矩 中心矩 总是零，表示分布的均值。

2.The fourth central moment 中心矩 relates to the kurtosis of the data set.

第四个中心矩 中心矩 与数据集的峰度有关。

3.Understanding the third central moment 中心矩 can help in assessing the skewness of a distribution.

理解第三个中心矩 中心矩 可以帮助评估分布的偏斜度。

4.When analyzing data, calculating the central moment 中心矩 can provide insights into its variability.

在分析数据时，计算中心矩 中心矩 可以提供对其变异性的洞察。

5.In statistics, the second central moment 中心矩 is known as the variance.

在统计学中，第二个中心矩 中心矩 被称为方差。

作文

In the study of statistics, the concept of a central moment is crucial for understanding the distribution of data. A central moment refers to the expected value of the deviations of a random variable from a fixed point, usually the mean. This statistical measure helps in assessing how much the values in a dataset vary from the central value, providing insights into the spread and shape of the distribution. The first central moment is always zero because it measures the distance from the mean itself. The second central moment, which is known as variance, quantifies the degree to which each number in a dataset differs from the mean and thus from every other number. A higher variance indicates that the numbers are more spread out, while a lower variance suggests that they are closer to the mean. Understanding the significance of central moments extends beyond mere calculations; it plays a vital role in various fields, including finance, psychology, and quality control. For instance, in finance, investors analyze the variance of stock returns to assess risk. A stock with high variance may be considered riskier, as its price can fluctuate significantly. On the other hand, a stock with low variance is seen as more stable. Thus, the second central moment becomes a key factor in portfolio management and investment strategies.Moreover, the third central moment, known as skewness, measures the asymmetry of the distribution. If the skewness is positive, it indicates that the tail on the right side of the distribution is longer or fatter than the left side, suggesting that there are extreme values on the higher end. Conversely, negative skewness indicates a longer or fatter tail on the left. Understanding skewness is essential for making informed decisions based on data, as it provides insights into potential outliers or anomalies within a dataset.The fourth central moment is called kurtosis, which measures the 'tailedness' of the distribution. High kurtosis indicates that a dataset has heavy tails or outliers, while low kurtosis suggests light tails. In many practical applications, such as finance and environmental studies, understanding kurtosis helps in assessing the likelihood of extreme events. For example, in risk management, knowing the kurtosis of financial returns can help analysts prepare for potential market crashes or booms.In conclusion, the central moment is not just a technical term used in statistics; it is a fundamental concept that aids in the interpretation and analysis of data. By examining the various central moments, researchers and professionals can gain a deeper understanding of the underlying patterns in their data, leading to more informed decisions and strategies. Whether in finance, social sciences, or any field that relies on data analysis, the importance of central moments cannot be overstated. They provide a framework for evaluating variability, risk, and the overall behavior of datasets, ultimately enhancing our ability to make sense of the world around us.

在统计学研究中，中心矩的概念对于理解数据的分布至关重要。中心矩指的是随机变量与固定点（通常是均值）偏差的期望值。这一统计量有助于评估数据集中值的变异程度，从而提供对分布的扩展和形状的洞察。第一个中心矩总是零，因为它测量的是与均值本身的距离。第二个中心矩，即方差，量化了数据集中每个数值与均值及其他数值的差异程度。较高的方差表明数值分散得更广，而较低的方差则暗示它们更接近均值。理解中心矩的重要性不仅限于计算，它在金融、心理学和质量控制等多个领域发挥着重要作用。例如，在金融领域，投资者分析股票收益的方差以评估风险。方差较高的股票可能被视为风险较大，因为其价格可能大幅波动。相反，方差较低的股票则被视为更稳定。因此，第二个中心矩成为投资组合管理和投资策略中的关键因素。此外，第三个中心矩被称为偏度，用于衡量分布的非对称性。如果偏度为正，则表示分布右侧的尾部比左侧更长或更粗，暗示在较高端存在极端值。相反，负偏度则表示左侧尾部更长或更粗。理解偏度对于根据数据做出明智决策至关重要，因为它提供了对数据集中潜在异常值或离群值的洞察。第四个中心矩称为峰度，它衡量分布的“尾部性”。高峰度表明数据集具有重尾或离群值，而低峰度则暗示轻尾。在许多实际应用中，例如金融和环境研究，了解峰度有助于评估极端事件的可能性。例如，在风险管理中，了解金融收益的峰度可以帮助分析师为潜在的市场崩溃或繁荣做好准备。总之，中心矩不仅仅是统计学中的一个技术术语；它是一个基本概念，有助于数据的解释和分析。通过考察各种中心矩，研究人员和专业人士可以更深入地理解数据背后的模式，从而做出更明智的决策和策略。无论是在金融、社会科学还是任何依赖数据分析的领域，中心矩的重要性都不容小觑。它们提供了评估变异性、风险和数据集整体行为的框架，最终增强了我们理解周围世界的能力。