gaussian distribution

简明释义

正态分布

英英释义

例句

1.The errors in measurements often exhibit a gaussian distribution (高斯分布).

测量中的误差通常表现出gaussian distribution（高斯分布）。

2.In statistics, the bell curve is often used to represent a gaussian distribution (高斯分布).

在统计学中，钟形曲线通常用于表示一个gaussian distribution（高斯分布）。

3.Many natural phenomena, like heights of people, follow a gaussian distribution (高斯分布).

许多自然现象，如人们的身高，遵循gaussian distribution（高斯分布）。

4.In machine learning, many algorithms assume that the data follows a gaussian distribution (高斯分布).

在机器学习中，许多算法假设数据遵循gaussian distribution（高斯分布）。

5.The central limit theorem states that the sum of many independent random variables will tend to a gaussian distribution (高斯分布).

中心极限定理表明，许多独立随机变量的和将趋向于gaussian distribution（高斯分布）。

作文

The concept of gaussian distribution is fundamental in the field of statistics and probability theory. It describes how the values of a variable are distributed, particularly when they cluster around a mean value. The gaussian distribution, also known as the normal distribution, is characterized by its bell-shaped curve, which is symmetric about the mean. This means that most of the observations fall close to the average, with fewer observations appearing as you move away from the center. Understanding the gaussian distribution is crucial for various applications, including data analysis, natural sciences, and social sciences.One of the most important properties of the gaussian distribution is the empirical rule, often referred to as the 68-95-99.7 rule. This rule states that approximately 68% of the data points will fall within one standard deviation of the mean, about 95% will fall within two standard deviations, and around 99.7% will lie within three standard deviations. This property allows researchers and analysts to make predictions about data sets and understand the variability within them. For example, if we know that a set of test scores follows a gaussian distribution, we can infer how many students are likely to score within a certain range, which is invaluable for educational assessments.Moreover, the gaussian distribution is widely used in the natural and social sciences. Many phenomena, such as heights, blood pressure, and measurement errors, tend to follow this distribution. In psychology and sociology, researchers often assume that certain traits or behaviors are normally distributed within a population. This assumption simplifies statistical analyses and helps in drawing conclusions from sample data. However, it is essential to verify whether the data truly follows a gaussian distribution before applying these statistical methods, as using the wrong distribution can lead to inaccurate results.In addition to its theoretical importance, the gaussian distribution has practical applications in various fields. For instance, in finance, stock returns are often assumed to be normally distributed, which aids in risk assessment and portfolio management. In quality control processes, manufacturers use the gaussian distribution to determine acceptable levels of variation in product dimensions. By understanding how products deviate from the mean, companies can maintain high-quality standards and minimize defects.Despite its widespread applicability, it is important to note that not all data follows a gaussian distribution. Some data sets exhibit skewness or kurtosis, which indicates that they deviate from the normal distribution. In these cases, alternative statistical models may be more appropriate. Researchers must conduct tests, such as the Shapiro-Wilk test or the Kolmogorov-Smirnov test, to assess the normality of their data before proceeding with analyses that assume a gaussian distribution.In conclusion, the gaussian distribution plays a vital role in statistics and various scientific disciplines. Its unique properties and characteristics make it an essential tool for understanding data behavior and making informed decisions based on statistical analysis. By mastering the concept of gaussian distribution, individuals can enhance their analytical skills and apply these principles effectively in real-world situations.

高斯分布的概念在统计学和概率论领域中是基础性的。它描述了一个变量的值是如何分布的，特别是当这些值围绕一个均值聚集时。高斯分布，也称为正态分布，以其钟形曲线为特征，该曲线相对于均值是对称的。这意味着大多数观察值接近平均值，而随着远离中心，观察值的数量逐渐减少。理解高斯分布对各种应用至关重要，包括数据分析、自然科学和社会科学。高斯分布最重要的特性之一是经验法则，通常称为68-95-99.7规则。该规则指出，大约68%的数据点将在均值的一个标准差内，约95%的数据点将在两个标准差内，而大约99.7%的数据点将在三个标准差内。这一特性使研究人员和分析师能够对数据集进行预测，并理解其中的变异性。例如，如果我们知道一组测试分数遵循高斯分布，我们可以推断出有多少学生可能会在某个范围内得分，这对教育评估来说是非常宝贵的。此外，高斯分布在自然科学和社会科学中被广泛使用。许多现象，如身高、血压和测量误差，往往遵循这种分布。在心理学和社会学中，研究人员通常假设某些特征或行为在一个群体中是正态分布的。这一假设简化了统计分析，并有助于从样本数据中得出结论。然而，在应用这些统计方法之前，务必验证数据是否确实遵循高斯分布，因为使用错误的分布可能导致不准确的结果。除了理论上的重要性，高斯分布在各个领域都有实际应用。例如，在金融领域，股票收益通常被假设为正态分布，这有助于风险评估和投资组合管理。在质量控制过程中，制造商使用高斯分布来确定产品尺寸的可接受变异水平。通过理解产品如何偏离均值，公司可以保持高质量标准并最小化缺陷。尽管高斯分布广泛适用，但需要注意的是，并非所有数据都遵循这种分布。一些数据集表现出偏斜或峰度，这表明它们偏离了正态分布。在这些情况下，其他统计模型可能更为合适。研究人员必须进行诸如Shapiro-Wilk检验或Kolmogorov-Smirnov检验等测试，以评估其数据的正态性，然后再进行假设为高斯分布的分析。总之，高斯分布在统计学和各种科学学科中发挥着至关重要的作用。它独特的属性和特征使其成为理解数据行为和基于统计分析做出明智决策的重要工具。通过掌握高斯分布的概念，个人可以增强他们的分析能力，并有效地将这些原理应用于现实世界的情况。