经典和贝叶斯推理新的四参数罗马克斯分布与应用程序
Mahreen Abdullah1, Muhammad Ahsan-Ul-Haq2, Abdullah M Alomair3
1School of Statistics, Minhaj University Lahore, Lahore Pakistan.
Heliyon
|February 22, 2024
概括
一个新的统计模型,新阿尔法功率转换功率洛马克斯分布,被开发用于分析生命周期数据. 这种灵活的分布为可靠性和生存分析提供了更好的性能.
科学领域:
- 统计 统计 统计 统计
- 可能性分布的概率分布.
- 可靠性工程可靠性工程
背景情况:
- 洛马克斯分布是一种广泛使用的概率模型,用于分析生命周期数据.
- 现有的洛马克斯分布模型可能缺乏灵活性,无法准确捕获复杂的生命周期数据模式.
- 需要新的统计分布来增强可靠性和生存数据的分析.
研究的目的:
- 使用阿尔法功率转换技术引入新的灵活的四参数罗马克斯分布.
- 推导和研究拟议分布的数学属性.
- 评估新分布在模拟现实世界生命周期数据中的性能.
主要方法:
- 新的阿尔法电力转换电力洛马克斯分布是数学上得出的.
- 获得了关键性质,包括时刻,量子函数和平均残余寿命.
- 用最大概率估计 (MLE) 和贝叶斯估计 (Metropolis-Hastings) 进行了参数估计.
- 模拟研究评估了MLE估计者的行为.
- 模型性能使用两个现实世界生命周期数据集进行了证明.
主要成果:
- 新阿尔法功率转换功率洛马克斯分布的数学属性已经成功得出.
- 模拟结果表明最大概率估计器的可靠性能.
- 与现有模型相比,拟议的分布在适应两个真实世界生命周期数据集方面表现出卓越的性能.
- 贝叶斯估计为模型参数提供了近似的贝叶斯估计.
结论:
- 新的阿尔法功率转换功率洛马克斯分布是对统计工具包的一项有价值的补充,用于终身数据分析.
- 拟议的模型为可靠性和生存数据提供了更高的灵活性和更好的解释性.
- 最大概率估计和贝叶斯方法都对新分布的参数估计有效.
相关概念视频
Distributions to Estimate Population Parameter
4.1K
The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...
4.1K
Model Approaches for Pharmacokinetic Data: Distributed Parameter Models
69
Pharmacokinetic models are mathematical constructs that represent and predict the time course of drug concentrations in the body, providing meaningful pharmacokinetic parameters. These models are categorized into compartment, physiological, and distributed parameter models.
The distributed parameter models are specifically designed to account for variations and differences in some drug classes. This model is particularly useful for assessing regional concentrations of anticancer or...
The distributed parameter models are specifically designed to account for variations and differences in some drug classes. This model is particularly useful for assessing regional concentrations of anticancer or...
69
Poisson Probability Distribution
8.1K
A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.
The...
The...
8.1K
One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation
502
This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
On...
On...
502
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
Maxwell-Boltzmann Distribution: Problem Solving
1.5K
Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
1.5K


