stable distribution

简明释义

稳定分布

英英释义

例句

1.Researchers often use a stable distribution 稳定分布 to fit data that exhibit heavy tails.

研究人员经常使用稳定分布 stable distribution来拟合表现出重尾特征的数据。

2.The stable distribution 稳定分布 is useful in telecommunications for modeling signal noise.

在电信领域，稳定分布 stable distribution对建模信号噪声非常有用。

3.In finance, the returns of certain assets can be modeled using a stable distribution 稳定分布 to account for extreme events.

在金融领域，某些资产的收益可以使用稳定分布 stable distribution来建模，以考虑极端事件。

4.In statistics, a stable distribution 稳定分布 can describe phenomena with non-Gaussian characteristics.

在统计学中，稳定分布 stable distribution可以描述具有非高斯特征的现象。

5.The central limit theorem applies to sums of random variables that follow a stable distribution 稳定分布 under certain conditions.

中心极限定理适用于在某些条件下遵循稳定分布 stable distribution的随机变量之和。

作文

In the realm of statistics and probability theory, the term stable distribution refers to a class of probability distributions that remain stable under the operation of convolution. This means that if you take two independent random variables that follow a stable distribution, their sum will also follow the same type of distribution, up to location and scale parameters. This property makes stable distribution an essential concept in various fields, including finance, physics, and telecommunications.One of the most notable characteristics of a stable distribution is that it can exhibit heavy tails, which means that it allows for extreme values or outliers. This feature contrasts with the more commonly used normal distribution, which has thin tails and does not account for extreme events effectively. For instance, in financial markets, asset returns often do not conform to the normal distribution due to the presence of sudden market crashes or spikes. Here, the use of stable distribution becomes crucial as it provides a more accurate model for such phenomena.The stable distribution family includes several well-known distributions, such as the Cauchy distribution and Lévy distribution. The Cauchy distribution, for example, is a type of stable distribution that does not have a defined mean or variance, making it particularly interesting in theoretical studies. In contrast, the Lévy distribution is often used in modeling processes involving jumps, such as stock prices or insurance claims, where large changes can occur suddenly.Understanding stable distribution is not only important for theoretical research but also for practical applications. In risk management, for instance, financial analysts utilize models based on stable distribution to forecast potential losses and assess the risk of investment portfolios. By acknowledging the likelihood of extreme events, analysts can make more informed decisions and develop strategies to mitigate risks effectively.Moreover, the concept of stable distribution extends beyond finance. In telecommunications, engineers apply these distributions to model packet arrival times, where data packets may arrive at irregular intervals, leading to bursts of traffic. This understanding helps in designing systems that can handle varying loads efficiently.In conclusion, the notion of stable distribution plays a pivotal role in both theoretical and applied statistics. Its unique properties, including the ability to model heavy-tailed phenomena, make it indispensable across various disciplines. As we continue to explore complex systems and data patterns, the relevance of stable distribution will undoubtedly grow, providing deeper insights into the nature of randomness and uncertainty in our world.

在统计学和概率论的领域中，术语稳定分布指的是一类在卷积运算下保持稳定的概率分布。这意味着，如果你取两个独立的随机变量，它们遵循稳定分布，那么它们的和也会遵循同一种类型的分布，只需调整位置和规模参数。这一特性使得稳定分布成为金融、物理和电信等多个领域的一个重要概念。稳定分布最显著的特征之一是它可以表现出重尾现象，这意味着它允许极端值或离群值的存在。这一特征与更常用的正态分布形成对比，后者具有薄尾，并不能有效地解释极端事件。例如，在金融市场中，资产收益通常不符合正态分布，因为存在突发的市场崩盘或激增。在这种情况下，使用稳定分布变得至关重要，因为它提供了更准确的模型来描述这些现象。稳定分布家族包括几个著名的分布，例如柯西分布和勒维分布。柯西分布例如，是一种类型的稳定分布，没有定义的均值或方差，这使其在理论研究中尤其有趣。相比之下，勒维分布通常用于建模涉及跳跃的过程，如股价或保险索赔，其中可能会突然发生大的变化。理解稳定分布不仅对理论研究重要，也对实际应用至关重要。在风险管理中，例如，金融分析师利用基于稳定分布的模型来预测潜在损失并评估投资组合的风险。通过承认极端事件的可能性，分析师可以做出更明智的决策，并制定有效的风险缓解策略。此外，稳定分布的概念超越了金融领域。在电信行业，工程师应用这些分布来建模数据包到达时间，其中数据包可能以不规则的间隔到达，导致流量的突发。这种理解有助于设计能够高效处理不同负载的系统。总之，稳定分布的概念在理论和应用统计学中扮演着关键角色。它独特的属性，包括建模重尾现象的能力，使其在多个学科中不可或缺。随着我们继续探索复杂系统和数据模式，稳定分布的重要性无疑将增长，为我们提供对随机性和不确定性本质的更深刻洞察。