On Jeffreys's cardioid distribution

IF 1.6 3区数学 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computational Statistics & Data Analysis Pub Date : 2025-07-16 DOI:10.1016/j.csda.2025.108248

Arthur Pewsey

引用次数: 0

Abstract

The cardioid distribution, despite being one of the fundamental models for circular data, has received limited attention both methodologically and in terms of its implementation in R. To redress these shortcomings, published results on the model are summarized, corrected and extended, and the scope and limitations of the existing support for the model in R identified. A thorough investigation into the performance of trigonometric moment and maximum likelihood based approaches to point and interval estimation of the model's location and concentration parameters is presented, and goodness-of-fit techniques outlined. A suite of reliable R functions is provided for the model's practical application. The application of the proposed inferential methods and R functions is illustrated by an analysis of palaeocurrent cross-bed azimuths.

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杰弗里斯的心脏分布

尽管心型分布是圆形数据的基本模型之一，但在方法上和在R中的实施方面都受到有限的关注。为了纠正这些缺点，对该模型的已发表结果进行了总结、修正和扩展，并确定了R中现有支持该模型的范围和局限性。深入研究了三角矩和基于最大似然的方法对模型的位置和浓度参数的点和区间估计的性能，并概述了拟合优度技术。为模型的实际应用提供了一套可靠的R函数。通过古水流交叉层方位角的分析，说明了所提出的推理方法和R函数的应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computational Statistics & Data Analysis 数学-计算机：跨学科应用

CiteScore

3.70

自引率

5.60%

发文量

167

审稿时长

60 days

期刊介绍： Computational Statistics and Data Analysis (CSDA), an Official Publication of the network Computational and Methodological Statistics (CMStatistics) and of the International Association for Statistical Computing (IASC), is an international journal dedicated to the dissemination of methodological research and applications in the areas of computational statistics and data analysis. The journal consists of four refereed sections which are divided into the following subject areas: I) Computational Statistics - Manuscripts dealing with: 1) the explicit impact of computers on statistical methodology (e.g., Bayesian computing, bioinformatics,computer graphics, computer intensive inferential methods, data exploration, data mining, expert systems, heuristics, knowledge based systems, machine learning, neural networks, numerical and optimization methods, parallel computing, statistical databases, statistical systems), and 2) the development, evaluation and validation of statistical software and algorithms. Software and algorithms can be submitted with manuscripts and will be stored together with the online article. II) Statistical Methodology for Data Analysis - Manuscripts dealing with novel and original data analytical strategies and methodologies applied in biostatistics (design and analytic methods for clinical trials, epidemiological studies, statistical genetics, or genetic/environmental interactions), chemometrics, classification, data exploration, density estimation, design of experiments, environmetrics, education, image analysis, marketing, model free data exploration, pattern recognition, psychometrics, statistical physics, image processing, robust procedures. [...] III) Special Applications - [...] IV) Annals of Statistical Data Science [...]