在概率分布中的不平等的基于的定位上
Rajeev Rajaram1, Nathan Ritchey1, Brian Castellani2
1Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USA.
Entropy (Basel, Switzerland)
|September 27, 2025
概括
我们开发了一种新方法,使用递归分解确定概率分布中的不平等. 这种技术揭示了不平等在哪里以及如何集中,为数据异质性提供了结构性见解.
科学领域:
- 信息理论 信息理论
- 统计分析 统计分析
- 数据科学数据科学数据科学
背景情况:
- 尺度总结通常会掩盖概率分布中的局部差异.
- 了解不平等的结构和度对于分析异质系统至关重要.
研究的目的:
- 引入一种用于在概率分布中定位不等式的新方法.
- 证明该方法在各种领域的适用性,包括统计和物理系统.
主要方法:
- 应用了一个递归的哈恩分解到统一度,从香农的指数推导.
- 将概率空间划分为不连接的区域,显示偏离统一性的偏差.
- 使用了正规分布 (二项式,指数式) 和假设示例 (疾病收缩,负载束).
主要成果:
- 成功地局部化了不平等,并确定了法典和应用系统中的结构差异.
- 在疾病收缩数据中揭示了流行病学差异的目标区域.
- 在负荷不均的束中发现应力局部,突出了与物理系统的相关性.
结论:
- 递归分解提供了信息不均的多尺度表示.
- 该框架为不平等的出现和局部化提供了结构性的洞察力.
- 对理解局部化和异质系统动态的潜在影响.
更多相关视频
08:13Using the Race Model Inequality to Quantify Behavioral Multisensory Integration Effects
Published on: May 10, 2019
6.8K
09:23Quantification of Information Encoded by Gene Expression Levels During Lifespan Modulation Under Broad-range Dietary Restriction in C. elegans
Published on: August 16, 2017
8.6K
相关概念视频
Probability Distributions
11.8K
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...
11.8K
Applications of Integration to Probability Density Functions
8
Continuous probability distributions are used to model random variables that can take on any real value within a specified range. These variables do not take on isolated or countable values but rather exist on a continuum. For example, the height of an individual can be measured with increasing precision—such as 163.5 or 165.25 centimeters—demonstrating that height is a continuous random variable.The behavior of such variables is described using a probability density function (PDF),...
8
Application of Nonlinear Inequalities
214
A nonlinear inequality describes a comparison involving an expression that curves or behaves more complexly than a straight line. These inequalities often appear in forms that include squares, products, or variables in the denominator.To solve such an inequality, one starts by rewriting it so that zero appears on one side. For example, the inequality: can be factored as: This form makes it easier to identify the values that cause the expression to equal zero. In this case, the...
214
Probability Histograms
13.2K
A probability histogram is a visual representation of a probability distribution. Similar a typical histogram, the probability histogram consists of contiguous (adjoining) boxes. It has both a horizontal axis and a vertical axis. The horizontal axis is labeled with what the data represents. The vertical axis is labeled with probability. Each rectangular bar in the histogram is 1 unit wide, which suggests that the area under each bar equals the probability, P(x), where x is 1, 2, 3, and so on.
13.2K
Binomial Probability Distribution
15.3K
A binomial distribution is a probability distribution for a procedure with a fixed number of trials, where each trial can have only two outcomes.
The outcomes of a binomial experiment fit a binomial probability distribution. A statistical experiment can be classified as a binomial experiment if the following conditions are met:
There are a fixed number of trials. Think of trials as repetitions of an experiment. The letter n denotes the number of trials.
There are only two possible outcomes,...
The outcomes of a binomial experiment fit a binomial probability distribution. A statistical experiment can be classified as a binomial experiment if the following conditions are met:
There are a fixed number of trials. Think of trials as repetitions of an experiment. The letter n denotes the number of trials.
There are only two possible outcomes,...
15.3K
Uniform Distribution
6.0K
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
6.0K
