poisson distribution

简明释义

泊松分布

英英释义

例句

1.The poisson distribution is useful for predicting the number of cars passing through a toll booth in an hour.

泊松分布对于预测一个小时内通过收费站的汽车数量非常有用。

2.When analyzing the number of accidents at a traffic intersection, a poisson distribution can be applied.

在分析交通交叉口事故数量时，可以应用泊松分布。

3.The number of emails received in an hour can be modeled using a poisson distribution.

每小时收到的邮件数量可以用泊松分布建模。

4.In a call center, the arrival of calls per minute follows a poisson distribution.

在呼叫中心，每分钟到达的电话数量遵循泊松分布。

5.The occurrence of rare events, such as earthquakes, can often be modeled with a poisson distribution.

稀有事件的发生，例如地震，通常可以用泊松分布建模。

作文

The concept of poisson distribution is fundamental in the field of statistics, especially when dealing with events that occur independently over a fixed period of time or space. Named after the French mathematician Siméon Denis Poisson, this probability distribution provides a mathematical framework for modeling the number of events that happen within a specified interval. Understanding the poisson distribution can greatly enhance our ability to analyze real-world phenomena, from the frequency of emails received in an hour to the number of phone calls at a call center during peak hours.In essence, the poisson distribution describes the probability of a given number of events occurring in a fixed interval of time or space, assuming these events happen with a known constant mean rate and are independent of the time since the last event. For instance, if we know that on average three cars pass through a toll booth every minute, we can use the poisson distribution to calculate the probability of observing a specific number of cars passing in any given minute.One of the key characteristics of the poisson distribution is its simplicity. It is defined by a single parameter, λ (lambda), which represents the average number of occurrences in the interval. The probability mass function of the poisson distribution is given by the formula P(X = k) = (λ^k * e^(-λ)) / k!, where P(X = k) is the probability of observing k events, e is the base of the natural logarithm, and k! is the factorial of k. This formula allows statisticians to calculate the likelihood of various outcomes, making it a powerful tool in predictive analysis.Moreover, the poisson distribution is applicable in a variety of fields. In healthcare, it can be used to model the number of patients arriving at an emergency room within a certain timeframe. In telecommunications, it helps in predicting the number of incoming calls to a service center. Even in environmental studies, it can assist in estimating the number of rare species in a given area.However, while the poisson distribution is incredibly useful, it is important to recognize its limitations. The assumption of independence between events may not hold true in all cases. For example, if a traffic accident occurs at a particular intersection, it might influence the likelihood of subsequent accidents in a short period of time. Therefore, analysts must carefully consider the context and ensure that the assumptions of the poisson distribution are met before applying it to their data.In conclusion, the poisson distribution is a vital statistical tool that aids in understanding and predicting the occurrence of events in various fields. Its ability to model random events effectively allows researchers and professionals to make informed decisions based on data. By mastering the principles of the poisson distribution, one can gain valuable insights into patterns and trends that might otherwise go unnoticed. As we continue to collect and analyze data in our increasingly complex world, the relevance of the poisson distribution will only grow, making it an essential topic for anyone interested in statistics or data science.

泊松分布的概念在统计学领域中是基础性的，特别是在处理在固定时间或空间内独立发生的事件时。泊松分布以法国数学家西门·德尼·泊松的名字命名，提供了一个数学框架，用于建模在特定区间内发生的事件数量。理解泊松分布可以大大增强我们分析现实世界现象的能力，从每小时收到的电子邮件频率到高峰时段呼叫中心的电话数量。本质上，泊松分布描述了在固定的时间或空间间隔内发生给定数量事件的概率，假设这些事件以已知的恒定平均速率发生，并且与上一个事件的时间独立。例如，如果我们知道平均每分钟有三辆车经过收费站，我们可以使用泊松分布来计算在任何给定一分钟内观察到特定数量汽车的概率。泊松分布的一个关键特征是其简单性。它由一个参数λ（lambda）定义，表示区间内的平均发生次数。泊松分布的概率质量函数由公式P(X = k) = (λ^k * e^(-λ)) / k!给出，其中P(X = k)是观察到k个事件的概率，e是自然对数的底数，k!是k的阶乘。这个公式使统计学家能够计算各种结果的可能性，使其成为预测分析中的强大工具。此外，泊松分布适用于多个领域。在医疗保健中，它可以用来建模在特定时间内到达急诊室的患者数量。在电信中，它有助于预测服务中心的来电数量。甚至在环境研究中，它可以帮助估算特定区域内稀有物种的数量。然而，尽管泊松分布极为有用，但重要的是要认识到其局限性。事件之间独立的假设在所有情况下可能并不成立。例如，如果某个交叉口发生交通事故，这可能会影响短时间内后续事故的可能性。因此，分析人员必须仔细考虑上下文，并确保在将泊松分布应用于数据之前满足其假设。总之，泊松分布是一个重要的统计工具，有助于理解和预测各个领域事件的发生。它有效建模随机事件的能力使研究人员和专业人士能够根据数据做出明智的决策。通过掌握泊松分布的原则，人们可以获得对模式和趋势的宝贵洞察，这些模式和趋势可能会被忽视。随着我们在日益复杂的世界中继续收集和分析数据，泊松分布的相关性只会增加，使其成为任何对统计或数据科学感兴趣的人的必修课题。