gaussian distribution

简明释义

高斯分布

英英释义

例句

1.In machine learning, many algorithms assume that the data is normally distributed, or follows a gaussian distribution 高斯分布.

在机器学习中，许多算法假设数据是正态分布的，或遵循 gaussian distribution 高斯分布。

2.When analyzing test scores, we often assume they follow a gaussian distribution 高斯分布 for simplification.

在分析考试成绩时，我们通常假设它们遵循 gaussian distribution 高斯分布 以简化计算。

3.Many natural phenomena, such as heights of people, follow a gaussian distribution 高斯分布 pattern.

许多自然现象，如人的身高，遵循 gaussian distribution 高斯分布 模式。

4.In statistics, the concept of gaussian distribution 高斯分布 is fundamental for understanding data behavior.

在统计学中，gaussian distribution 高斯分布 的概念对于理解数据行为是基础。

5.The errors in measurement often exhibit a gaussian distribution 高斯分布, indicating that most errors are small.

测量中的误差通常表现出 gaussian distribution 高斯分布，这表明大多数误差很小。

作文

The concept of gaussian distribution is fundamental in the field of statistics and probability theory. Often referred to as the normal distribution, it describes how the values of a variable are distributed. The gaussian distribution is characterized by its bell-shaped curve, which is symmetric around the mean. This symmetry indicates that most of the observations cluster around the central peak, with probabilities for values further away from the mean tapering off equally in both directions. Understanding the gaussian distribution is crucial because many statistical methods assume that data follows this distribution. For example, in quality control, the measurements of products often follow a gaussian distribution, making it easier to identify defects when they fall outside the expected range. Additionally, the gaussian distribution is significant in the Central Limit Theorem, which states that the sum of a large number of independent random variables, regardless of their original distribution, will tend to be normally distributed. This theorem underpins many statistical practices and justifies the use of the gaussian distribution in various fields, including economics, psychology, and natural sciences.The mathematical representation of the gaussian distribution involves 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 or dispersion of the data. A smaller standard deviation results in a steeper curve, indicating that the data points are closer to the mean. In contrast, a larger standard deviation produces a flatter curve, suggesting more variability among the data points. In practical applications, the gaussian distribution helps in making predictions and decisions. For instance, in finance, analysts often assume that stock returns are normally distributed when evaluating risks and making investment decisions. By using the properties of the gaussian distribution, they can calculate confidence intervals and assess the likelihood of different outcomes. Moreover, the gaussian distribution is not only limited to theoretical studies but also plays a vital role in real-world scenarios. In education, standardized test scores are frequently modeled using the gaussian distribution. This approach allows educators to understand how students perform relative to their peers, identifying those who may need additional support or enrichment. Similarly, in healthcare, biological measurements such as blood pressure and cholesterol levels often exhibit a gaussian distribution, enabling doctors to make informed decisions based on population averages. Despite its widespread applicability, it is essential to recognize that not all datasets follow a gaussian distribution. Some data may exhibit skewness or kurtosis, leading to deviations from the normality assumption. In such cases, alternative distributions may be more appropriate for analysis. Nevertheless, the gaussian distribution remains a powerful tool in statistics, providing a foundation for understanding variability and making inferences about populations based on sample data. In conclusion, the gaussian distribution is a pivotal concept in statistics that influences various disciplines. Its properties facilitate data analysis and interpretation, making it indispensable for researchers and practitioners alike. By grasping the essence of the gaussian distribution, one can better appreciate its significance in both theoretical and applied contexts.

“高斯分布”这一概念在统计学和概率论领域中具有基础性的重要性。通常被称为正态分布，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，围绕均值对称。这种对称性表明，大多数观察值聚集在中央峰值附近，而远离均值的值的概率则在两个方向上均匀递减。理解“高斯分布”至关重要，因为许多统计方法假设数据遵循这种分布。例如，在质量控制中，产品的测量值通常遵循“高斯分布”，这使得在预期范围之外识别缺陷变得更加容易。此外，“高斯分布”在中心极限定理中也具有重要意义，该定理指出，无论原始分布如何，大量独立随机变量的和将趋向于正态分布。该定理为许多统计实践提供了基础，并证明了在经济学、心理学和自然科学等多个领域使用“高斯分布”的合理性。“高斯分布”的数学表示涉及两个参数：均值（μ）和标准差（σ）。均值确定分布的中心，而标准差则衡量数据的分散程度。较小的标准差会导致曲线更陡峭，表明数据点更接近均值。相反，较大的标准差会产生更平坦的曲线，表明数据点之间的变异性更大。在实际应用中，“高斯分布”有助于做出预测和决策。例如，在金融领域，分析师通常假设股票收益呈正态分布，以评估风险并做出投资决策。通过利用“高斯分布”的属性，他们可以计算置信区间并评估不同结果的可能性。此外，“高斯分布”不仅限于理论研究，还在现实场景中发挥着重要作用。在教育领域，标准化考试成绩通常使用“高斯分布”建模。这种方法使教育者能够了解学生相对于同龄人的表现，从而识别出需要额外支持或提高的学生。同样，在医疗保健中，生物测量如血压和胆固醇水平通常表现出“高斯分布”，使医生能够根据人口平均水平做出明智的决定。尽管其广泛适用，但必须认识到，并非所有数据集都遵循“高斯分布”。一些数据可能表现出偏斜或峰度，导致偏离正态性假设。在这种情况下，替代分布可能更适合进行分析。然而，“高斯分布”仍然是统计学中的一种强大工具，为理解变异性和基于样本数据对总体进行推断提供了基础。总之，“高斯分布”是统计学中的一个关键概念，对各个学科都有影响。其特性促进了数据分析和解释，使其对研究人员和从业人员来说不可或缺。通过掌握“高斯分布”的本质，人们可以更好地理解其在理论和应用背景下的重要性。