在决定性的混乱地图中正常分布的出现
Damián H Zanette1,2, Inés Samengo1,2
1Instituto Balseiro, Centro Atómico Bariloche Comisión Nacional de Energía Atómica, Universidad Nacional de Cuyo, Av. Ezequiel Bustillo 9500, San Carlos de Bariloche 8400, Argentina.
Entropy (Basel, Switzerland)
|January 22, 2024
概括
本研究探讨了对依赖变量的中央极限定理,发现收速度比独立变量慢. 系统特定的因素,如混合强度和分布尾巴,会影响这种趋同发生的速度.
科学领域:
- 概率理论的概率理论是什么
- 统计力学就是统计力学.
- 动态系统是动态系统.
背景情况:
- 中央极限定理 (CLT) 描述了独立随机变量的和到稳定的分布的趋同.
- 现实世界的系统往往表现出依赖性,限制了标准CLT的直接适用性.
- 之前的工作已经将CLT扩展到非独立变量,但对收动态的表征仍然至关重要.
研究的目的:
- 为了数值地描述决定性相关变量的中央极限定理的收.
- 为了研究融合速度如何在不同的ergodic映射和系统属性之间变化.
- 在总和过程中识别影响确定性信息丢失的因素.
主要方法:
- 由ergodic映射生成的随机变量和的数值模拟.
- 对临界分布的收率的分析.
- 研究系统特异性因素,如混合强度和边际分布形状.
主要成果:
- 对于依赖变量而言,与独立变量相比,对极限分布的趋同始终较慢.
- 在不同的决定性系统中,收率有很大差异.
- 诸如映射的混合强度和边缘分布中脂肪尾的存在等因素,极大地影响了趋同速度.
结论:
- 对于依赖变量的CLT趋同得更慢,其动态是由系统属性决定的.
- 了解这些依赖关系是准确建模系统的关键,在这些系统中,独立性并未得到保证.
- 该研究强调了映射特征和分布性质在依赖随机变量和的行为中的重要性.
相关概念视频
Probability Distributions
7.0K
The probability of a random variable x is the likelihood of its occurrence. A probability distribution represents the probabilities of a random variable using a formula, graph, or table. There are two types of probability distribution– discrete probability distribution and continuous probability distribution.
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson...
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson...
7.0K
Normal Distribution
10.9K
The normal, a continuous distribution, is the most important of all the distributions. Its graph is a bell-shaped symmetrical curve, which is observed in almost all disciplines. Some of these include psychology, business, economics, the sciences, nursing, and, of course, mathematics. Some instructors may use the normal distribution to help determine students’ grades. Most IQ scores are normally distributed. Often real-estate prices fit a normal distribution. The normal distribution is...
10.9K
Applications of Normal Distribution
5.1K
The normal distribution is a useful statistical tool. One of its practical applications is determining the door height after considering the normal distribution of heights of persons, such that many can pass through it easily without striking their heads. The normal distribution can also determine the probability of a person having a height less than a specific height.
The heights of 15 to 18-year-old males from Chile from 1984 to 1985 followed a normal distribution. The mean height is 172.36...
The heights of 15 to 18-year-old males from Chile from 1984 to 1985 followed a normal distribution. The mean height is 172.36...
5.1K
Central Limit Theorem
14.8K
The central limit theorem, abbreviated as clt, is one of the most powerful and useful ideas in all of statistics. The central limit theorem for sample means says that if you repeatedly draw samples of a given size and calculate their means, and create a histogram of those means, then the resulting histogram will tend to have an approximate normal bell shape. In other words, as sample sizes increase, the distribution of means follows the normal distribution more closely.
The sample size, n, that...
The sample size, n, that...
14.8K
Uniform Distribution
5.0K
The uniform distribution is a continuous probability distribution of events with an equal probability of occurrence. This distribution is rectangular.
Two essential properties of this distribution are
Two essential properties of this distribution are
5.0K
The Bell Curve
201
The normal probability distribution, often depicted as a symmetrical, bell-shaped curve, is fundamental in statistics and the study of natural phenomena. This pattern, famously described by mathematician Carl Friedrich Gauss, shows how data points are distributed around a central mean, with most values near the average and fewer observations occurring as they deviate further from it.
This pattern applies to many human characteristics beyond intelligence, such as height. For example, if you...
This pattern applies to many human characteristics beyond intelligence, such as height. For example, if you...
201


