Using Bayesian Analysis and Maximum Entropy To Develop Non‐parametric Probability Distributions for the Mean and Variance
作者:
William J. Price,
Harold J. Price,
Bahman Shafii,
期刊:
AIP Conference Proceedings
(AIP Available online 1903)
卷期:
Volume 659,
issue 1
页码: 53-61
ISSN:0094-243X
年代: 1903
DOI:10.1063/1.1570534
出版商: AIP
数据来源: AIP
摘要:
Estimation of the population mean, and variance is generally carried out using sample estimates. Given normality of the parent population, the distribution of sample mean and sample variance is straightforward. However, when normality cannot be assumed, inference is usually based on approximations through the use of the Central Limit theorem. In addition, the data generated from many real populations may be naturally bounded, i.e. weights, heights, etc. Thus, the unbounded normal probability model may not be appropriate. Utilizing Bayesian analysis and maximum entropy, procedures are developed which produce nonparametric distributions for both the mean and the mean/standard deviation combination. These methods require no assumptions on the form of the parent distribution or the size of the sample and inherently make use of existing bounds. © 2003 American Institute of Physics
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