Comparison of estimation methods of the joint density of a circular and linear variable

Sahana Bhattacharjee ； Kishore Kumar Das

《Journal of Data Science》 15卷1期 (2017/01) Pp. 129-154

https://doi.org/10.6339/JDS.201701_15(1).0008

摘要

A detailed account on environment and its related problems often requires a study on variables, some of which may be linear and others, circular in nature. Specialized techniques are required to analyze circular variables and also, the interrelationship between circular and linear variable. In this paper, estimation methods of joint density of a circular and linear variable have been compared with the aid of three real life examples. Therein, we have computed the maximum likelihood estimates of the l-modal circular normal distribution and used the Monte Carlo approximation method to approximate its distribution function. Finally, the theory of Copula function has been put to use for exploring the association between the two variables. The study reveals the superiority of one of the methods over the others, as exemplified by all the three data sets.

關鍵字

l-modal circular normal distribution ； Maximum Likelihood Estimation ； Monte Carlo Approximation ； Comparison of Circular-linear joint density estimation methods ； Copula function