On Jeffreys's cardioid distribution
系统梳理、修正并扩展了Jeffreys心形分布的理论结果，评估了R语言中现有支持的不足，提供了基于三角矩和最大似然的点估计与区间估计方法，并开发了实用的R函数包，通过古水流数据示例展示应用。
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. • Provides a thorough review of the published results on Jeffreys's cardioid model, which are then corrected and extended. • Identifies the scope and limitations of the existing support for the cardioid model in R. • Presents a thorough investigation of trigonometric moment and maximum likelihood based point and interval estimation. • Outlines techniques which can be used to investigate the goodness-of-fit of the cardioid model. • Provides a suite of reliable R functions for the cardioid model's application.