Birnbaum-Saunders 分布百分位数之间差异的广义可信区间及其在泰国 PM2.5 中的应用

IF 0.9 Q3 MATHEMATICS, APPLIED
Warisa Thangjai, Sa-Aat Niwitpong, Suparat Niwitpong
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引用次数: 0

摘要

Birnbaum-Saunders 分布对统计推断特别重要。该分布代表了工程学中的故障时间分布。此外,Birnbaum-Saunders 分布还常用于科学和工程学的不同领域。百分位数是一个经常使用的统计概念。百分位数有助于确定一个观测点在低于该观测点的数据点百分比中所处的位置。这些百分位数可作为数据的中心倾向和分散程度的指标。在比较两个数据分布时,平均值通常是描述总体最可靠的参数。不过,在分布呈现明显偏斜的情况下,百分位数有时可能提供更可靠的表示。本文采用广义置信区间(GCI)方法、自引导方法、贝叶斯方法和最高后验密度(HPD)方法构建了 Birnbaum-Saunders 分布百分位数之间差异的置信区间。为评估置信区间的性能,进行了蒙特卡罗模拟。性能通过覆盖概率和平均宽度进行考量。研究结果表明,利用 GCI 方法估计两个百分位数之间差距的置信区间是可取的。最后,概述了模拟调查的结果以及在环境科学领域的应用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Generalized Confidence Interval for the Difference Between Percentiles of Birnbaum–Saunders Distributions and Its Application to PM2.5 in Thailand

Generalized Confidence Interval for the Difference Between Percentiles of Birnbaum–Saunders Distributions and Its Application to PM2.5 in Thailand

The Birnbaum–Saunders distribution is of particular interest for statistical inference. This distribution represents the failure time distribution in engineering. In addition, the Birnbaum–Saunders distribution is commonly used in different areas of science and engineering. Percentiles are a frequently employed statistical concept. Percentiles help ascertain the position of an observation concerning the percentage of data points below it. These percentiles serve as indicators of both the central tendency and the dispersion of data. While comparing two data distributions, the mean is typically the most dependable parameter for describing the population. However, in situations where the distribution exhibits significant skewness, percentiles may sometimes offer a more reliable representation. Herein, the confidence intervals for the difference between percentiles of Birnbaum–Saunders distributions were constructed by the generalized confidence interval (GCI) approach, the bootstrap approach, the Bayesian approach, and the highest posterior density (HPD) approach. A Monte Carlo simulation was conducted to evaluate the performance of the confidence intervals. The performance was considered via coverage probability and average width. The findings suggest that utilizing the GCI approach is advisable for estimating confidence intervals for the disparity between two percentiles. Ultimately, the outcomes of the simulation investigation, coupled with an application in the field of environmental sciences, were outlined.

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