lognormal distribution

简明释义

对数正态分布;

英英释义

例句

1.The income levels in this region follow a lognormal distribution, which indicates that most people earn low to moderate incomes, with a few earning significantly more.

该地区的收入水平遵循对数正态分布，这表明大多数人赚取低到中等的收入，而少数人赚取显著更高的收入。

2.When analyzing the distribution of city sizes, researchers found that they fit a lognormal distribution, indicating that smaller cities are much more common than larger ones.

在分析城市规模的分布时，研究人员发现它们符合对数正态分布，这表明较小的城市比较大的城市更为常见。

3.The lengths of fish in a certain lake were observed to follow a lognormal distribution, suggesting that most fish are relatively small, with a few reaching large sizes.

在某个湖泊中观察到鱼的长度遵循对数正态分布，这表明大多数鱼相对较小，而少数鱼则达到较大的尺寸。

4.The time it takes for a computer to complete a task can be represented by a lognormal distribution, reflecting that most tasks are completed quickly, while a few take much longer.

计算机完成任务所需的时间可以用对数正态分布表示，这反映出大多数任务快速完成，而少数任务则需要更长的时间。

5.In finance, stock prices are often modeled using a lognormal distribution because they cannot be negative and tend to grow exponentially.

在金融中，股票价格通常使用对数正态分布进行建模，因为它们不能为负值，并且往往呈指数增长。

作文

The concept of lognormal distribution is essential in various fields such as finance, environmental studies, and engineering. A random variable is said to follow a lognormal distribution if its logarithm is normally distributed. This means that if we take the natural logarithm of a variable that follows a lognormal distribution, the result will be a normal distribution. This characteristic makes the lognormal distribution particularly useful for modeling data that are positively skewed, where values cannot be negative, such as stock prices or income levels.In finance, for example, the returns on stocks are often modeled using the lognormal distribution. This is because stock prices cannot fall below zero, and their logarithmic returns tend to be normally distributed over time. Investors use this model to gauge the risk and potential return of their investments. By understanding the lognormal distribution, they can make informed decisions about asset allocation and risk management.Moreover, the lognormal distribution plays a significant role in environmental studies, especially when dealing with pollutants or concentrations of substances in the environment. For instance, the concentration of certain contaminants in soil or water often follows a lognormal distribution. This means that while most samples may have low concentrations, there can be a few samples with extremely high concentrations. Understanding this distribution helps in assessing risks to human health and the environment.One of the key features of the lognormal distribution is its parameters. The distribution is characterized by two parameters: the mean and the standard deviation of the variable's logarithm. These parameters influence the shape of the distribution curve. A small standard deviation indicates that the data points are closely clustered around the mean, while a larger standard deviation suggests a wider spread of values. This flexibility allows researchers and analysts to adapt the lognormal distribution to fit various datasets accurately.In addition, the lognormal distribution is often contrasted with the normal distribution. While the normal distribution is symmetric, the lognormal distribution is skewed to the right. This asymmetry is crucial when analyzing real-world data, as many phenomena exhibit this type of behavior. For instance, wealth distribution among individuals typically follows a lognormal distribution, where a small number of people hold a large portion of the total wealth, while the majority possess much less.Understanding the lognormal distribution also involves recognizing its applications in risk assessment and management. In industries like insurance, the lognormal distribution can help actuaries predict the likelihood of extreme events and their financial impacts. By modeling claims and losses using the lognormal distribution, companies can set premiums and reserves more accurately.In conclusion, the lognormal distribution is a powerful statistical tool that finds applications across various disciplines. Its unique characteristics allow it to model data that is positively skewed and bounded below by zero. By mastering the lognormal distribution, professionals in finance, environmental science, and other fields can enhance their analytical capabilities and make better-informed decisions based on the underlying data patterns.

在金融、环境研究和工程等多个领域，对数正态分布的概念至关重要。如果一个随机变量的对数是正态分布的，那么这个变量就被称为遵循对数正态分布。这意味着，如果我们对遵循对数正态分布的变量取自然对数，结果将是正态分布。这一特性使得对数正态分布特别适合用于建模那些正偏态的数据，其中值不能为负，例如股票价格或收入水平。例如，在金融学中，股票的回报率通常使用对数正态分布进行建模。这是因为股票价格不能低于零，并且它们的对数回报率随着时间的推移往往呈正态分布。投资者利用这一模型来评估投资的风险和潜在回报。通过理解对数正态分布，他们可以对资产配置和风险管理做出明智的决策。此外，对数正态分布在环境研究中也发挥着重要作用，尤其是在处理污染物或环境中物质浓度时。例如，某些污染物在土壤或水中的浓度通常遵循对数正态分布。这意味着虽然大多数样本可能具有低浓度，但也可能有少数样本具有极高的浓度。理解这种分布有助于评估对人类健康和环境的风险。对数正态分布的一个关键特征是其参数。该分布由两个参数定义：变量对数的均值和标准差。这些参数影响分布曲线的形状。小的标准差表示数据点紧密聚集在均值附近，而较大的标准差则表明值的分布更广泛。这种灵活性使研究人员和分析师能够准确地调整对数正态分布以适应各种数据集。此外，对数正态分布通常与正态分布进行对比。尽管正态分布是对称的，但对数正态分布则向右偏斜。这种不对称性在分析现实世界数据时至关重要，因为许多现象表现出这种行为。例如，个人财富的分布通常遵循对数正态分布，其中少数人拥有大部分财富，而大多数人则拥有的财富要少得多。理解对数正态分布还涉及到识别其在风险评估和管理中的应用。在保险等行业中，对数正态分布可以帮助精算师预测极端事件及其财务影响的可能性。通过使用对数正态分布对索赔和损失进行建模，公司可以更准确地设定保费和准备金。总之，对数正态分布是一个强大的统计工具，在多个学科中都有应用。它独特的特性使其能够建模那些正偏态且下限为零的数据。通过掌握对数正态分布，金融、环境科学和其他领域的专业人士可以增强他们的分析能力，并根据潜在的数据模式做出更明智的决策。