Gaussian distribution

简明释义

正态分布

英英释义

例句

1.In finance, asset returns are often assumed to follow a Gaussian distribution (高斯分布) for modeling purposes.

在金融领域，资产收益通常被假定遵循高斯分布（高斯分布）以进行建模。

2.In statistics, the heights of a large group of people often follow a Gaussian distribution (高斯分布), where most individuals are around the average height.

在统计学中，一大群人的身高往往遵循高斯分布（高斯分布），大多数人的身高接近平均值。

3.The errors in measurements can usually be modeled with a Gaussian distribution (高斯分布) due to random fluctuations.

由于随机波动，测量中的误差通常可以用高斯分布（高斯分布）来建模。

4.Many natural phenomena, such as test scores, approximate a Gaussian distribution (高斯分布) when a large number of samples are taken.

许多自然现象，例如考试成绩，当取样数量很大时，近似于高斯分布（高斯分布）。

5.Machine learning algorithms frequently assume that the features of the data are normally distributed, which is another term for Gaussian distribution (高斯分布).

机器学习算法经常假设数据的特征是正态分布，这也是高斯分布（高斯分布）的另一个术语。

作文

The concept of Gaussian distribution, also known as the normal distribution, is fundamental in statistics and probability theory. It describes how the values of a variable are distributed. The Gaussian distribution is characterized by its bell-shaped curve, which is symmetrical about the mean. This distribution is significant because it appears in various natural phenomena, making it a crucial tool for data analysis and interpretation.In many real-world situations, we observe that data tends to cluster around a central value with no bias left or right. For example, if we were to measure the heights of a large group of people, we would likely find that most individuals fall within a certain range around the average height, with fewer individuals being significantly taller or shorter. This pattern can be effectively modeled using the Gaussian distribution.One of the key properties of the Gaussian distribution is that it is defined by two parameters: the mean (µ) and the standard deviation (σ). The mean determines the center of the distribution, while the standard deviation measures the spread of the data around the mean. A small standard deviation indicates that the data points tend to be close to the mean, while a larger standard deviation suggests a wider spread of values.The importance of the Gaussian distribution extends beyond theoretical applications; it is widely used in practical scenarios such as quality control, finance, and social sciences. In quality control, for instance, manufacturers use the Gaussian distribution to monitor product dimensions and ensure they remain within specified limits. Any significant deviations from the mean can indicate potential defects in the manufacturing process.In finance, the Gaussian distribution is used to model asset returns and assess risk. Investors often assume that the returns on their investments follow a normal distribution, which allows them to make informed decisions based on the expected performance of their portfolios. However, it is essential to recognize that financial markets can exhibit behaviors that deviate from this assumption, leading to the emergence of alternative models that account for these anomalies.Moreover, the Gaussian distribution plays a critical role in the field of machine learning. Many algorithms, such as linear regression and support vector machines, assume that the underlying data follows a normal distribution. Understanding the properties of the Gaussian distribution helps data scientists preprocess data effectively, optimize model performance, and interpret results accurately.Despite its widespread applicability, it is important to note that not all datasets conform to the Gaussian distribution. Some data may exhibit skewness or kurtosis, implying that other statistical distributions may be more appropriate for modeling. Therefore, it is crucial for researchers and analysts to conduct exploratory data analysis to understand the underlying structure of their data before applying the Gaussian distribution or any other statistical model.In conclusion, the Gaussian distribution is a cornerstone of statistical analysis, providing valuable insights into the behavior of random variables. Its properties and applications span various fields, from natural sciences to finance and machine learning. By understanding the Gaussian distribution, individuals can enhance their analytical skills and make more informed decisions based on data-driven insights. As we continue to explore complex datasets, the Gaussian distribution will remain an essential tool in our statistical toolkit, guiding us in our quest for knowledge and understanding of the world around us.

“高斯分布”的概念，也称为正态分布，是统计学和概率论中的基础。它描述了一个变量的值是如何分布的。“高斯分布”的特征是其钟形曲线，该曲线关于均值对称。这种分布之所以重要，是因为它出现在各种自然现象中，使其成为数据分析和解释的关键工具。在许多现实情况中，我们观察到数据往往聚集在一个中心值附近，左右没有偏差。例如，如果我们测量一大群人的身高，我们可能会发现大多数人落在某个平均身高范围内，而极少数人明显更高或更矮。这个模式可以有效地用“高斯分布”建模。“高斯分布”的一个关键特性是它由两个参数定义：均值（µ）和标准差（σ）。均值决定了分布的中心，而标准差则衡量数据围绕均值的分散程度。小的标准差表明数据点倾向于接近均值，而较大的标准差则暗示值的分布更广。“高斯分布”的重要性不仅限于理论应用；它在质量控制、金融和社会科学等实际场景中被广泛使用。例如，在质量控制中，制造商使用“高斯分布”来监控产品尺寸，并确保其保持在指定限制内。任何显著偏离均值的情况都可能表明制造过程中潜在的缺陷。在金融领域，“高斯分布”用于建模资产收益和评估风险。投资者通常假设他们的投资回报遵循正态分布，这使他们能够根据投资组合的预期表现做出明智的决策。然而，必须认识到，金融市场可能表现出偏离这一假设的行为，从而导致出现其他模型，以解释这些异常现象。此外，“高斯分布”在机器学习领域也起着至关重要的作用。许多算法，如线性回归和支持向量机，假设基础数据遵循正态分布。理解“高斯分布”的特性有助于数据科学家有效地预处理数据，优化模型性能并准确解释结果。尽管“高斯分布”具有广泛的适用性，但重要的是要注意，并非所有数据集都符合“高斯分布”。某些数据可能表现出偏斜或峰度，这意味着其他统计分布可能更适合建模。因此，研究人员和分析师在应用“高斯分布”或任何其他统计模型之前，进行探索性数据分析以了解数据的基本结构至关重要。总之，“高斯分布”是统计分析的基石，为随机变量的行为提供了宝贵的见解。它的属性和应用跨越多个领域，从自然科学到金融和机器学习。通过理解“高斯分布”，个人可以增强他们的分析能力，并根据数据驱动的见解做出更明智的决策。随着我们继续探索复杂的数据集，“高斯分布”将仍然是我们统计工具箱中的一个重要工具，指导我们在追求知识和理解周围世界的过程中。