sample central moments

简明释义

样本中心矩

英英释义

例句

1.To assess variability in a dataset, we can compute the second sample central moments 样本中心矩.

为了评估数据集中的变异性，我们可以计算第二个样本中心矩 样本中心矩。

2.The third sample central moments 样本中心矩 helps us identify skewness in the data distribution.

第三个样本中心矩 样本中心矩帮助我们识别数据分布的偏斜。

3.In statistics, we often calculate the sample central moments 样本中心矩 to understand the distribution of data.

在统计学中，我们经常计算样本中心矩 样本中心矩以了解数据的分布。

4.The first sample central moments 样本中心矩 is always zero, as it measures the mean deviation from the mean.

第一个样本中心矩 样本中心矩总是零，因为它衡量的是均值的偏差。

5.When analyzing financial returns, calculating the fourth sample central moments 样本中心矩 can indicate kurtosis.

在分析金融收益时，计算第四个样本中心矩 样本中心矩可以指示峰度。

作文

In the field of statistics, understanding data is crucial for making informed decisions. One of the fundamental concepts that statisticians often use is the idea of moments. Among these, sample central moments are particularly significant as they provide insights into the distribution and variability of a dataset. To grasp the importance of sample central moments, we must first explore what moments are in statistical terms. Moments are quantitative measures that describe the shape of a probability distribution. The first moment is the mean, which gives us the average value of the data. The second moment about the mean is the variance, which measures how spread out the values are around the mean. Higher-order moments, such as skewness and kurtosis, provide further information about the asymmetry and peakedness of the distribution, respectively. Now, when we refer to sample central moments, we are specifically talking about moments calculated from a sample rather than an entire population. This distinction is essential because, in most practical scenarios, we only have access to a sample of data rather than the complete dataset. The sample central moments allow us to estimate the characteristics of the population from which the sample is drawn. The first sample central moment is always zero since it is centered around the mean. The second sample central moment, which is related to variance, helps us understand the dispersion of our data points. A larger variance indicates that the data points are more spread out from the mean, while a smaller variance suggests that they are closely clustered around the mean. The third sample central moment relates to skewness, which tells us whether the data distribution is symmetrical or not. If the skewness is positive, it means that the tail on the right side of the distribution is longer or fatter than the left side, indicating that there are some unusually high values in the dataset. Conversely, a negative skewness suggests that the left tail is longer or fatter, indicating the presence of unusually low values. Finally, the fourth sample central moment corresponds to kurtosis, which describes the 'tailedness' of the distribution. A high kurtosis value indicates that the distribution has heavier tails and a sharper peak compared to a normal distribution, while a low kurtosis value suggests lighter tails and a flatter peak. Understanding these aspects of sample central moments is vital for statisticians and researchers, as they influence the choice of statistical tests and methods used for data analysis. In conclusion, sample central moments are indispensable tools in statistics that help us summarize and interpret data effectively. By calculating these moments, we can gain valuable insights into the characteristics of our data, which ultimately aids in making informed decisions based on statistical analysis. As we continue to collect and analyze data in various fields, the significance of sample central moments will only grow, emphasizing the need for a solid understanding of this concept in the realm of statistics.

在统计学领域，理解数据对于做出明智的决策至关重要。统计学家经常使用的基本概念之一是矩的概念。在这些矩中，样本中心矩尤其重要，因为它们提供了对数据集分布和变异性的洞察。要理解样本中心矩的重要性，我们首先必须探讨矩在统计学中的含义。矩是定量度量，用于描述概率分布的形状。第一个矩是均值，它给出了数据的平均值。关于均值的第二个矩是方差，它测量数据点围绕均值的分散程度。更高阶的矩，如偏度和峰度，提供了关于分布的非对称性和尖锐度的进一步信息。现在，当我们提到样本中心矩时，我们特别指的是从样本中计算的矩，而不是整个总体。这一区别至关重要，因为在大多数实际情况下，我们只能访问一部分数据，而不是完整的数据集。样本中心矩使我们能够估计从中抽取样本的总体特征。第一个样本中心矩始终为零，因为它是围绕均值中心的。第二个样本中心矩与方差相关，帮助我们理解数据点的分散情况。较大的方差表明数据点在均值周围更分散，而较小的方差则表明它们紧密聚集在均值附近。第三个样本中心矩与偏度相关，它告诉我们数据分布是否对称。如果偏度为正，则意味着分布右侧的尾部比左侧的尾部更长或更粗，表明数据集中存在一些异常高值。相反，负偏度则表明左侧尾部更长或更粗，暗示存在异常低值。最后，第四个样本中心矩对应于峰度，描述了分布的“尾部特性”。高峰度值表明分布具有比正态分布更重的尾部和更尖的峰，而低峰度值则表明尾部更轻且峰更平。理解这些样本中心矩的各个方面对统计学家和研究人员至关重要，因为它们会影响用于数据分析的统计检验和方法的选择。总之，样本中心矩是统计学中不可或缺的工具，帮助我们有效地总结和解释数据。通过计算这些矩，我们可以获得有关数据特征的宝贵见解，从而有助于基于统计分析做出明智的决策。随着我们在各个领域继续收集和分析数据，样本中心矩的重要性只会增加，这强调了在统计学领域对这一概念的深入理解的必要性。