# The wrapped xgamma distribution for modeling circular data appearing in geological context

## TL;DR

This paper introduces a wrapped xgamma distribution for modeling circular data, explores its properties, estimates parameters via maximum likelihood, and demonstrates its application on geological data, outperforming other circular models.

## Contribution

The paper presents the first circular xgamma distribution, extending univariate distribution theory to circular data with estimation and real-world application.

## Key findings

- The wrapped xgamma distribution fits geological circular data well.
- Maximum likelihood estimates are effective for parameter inference.
- The new distribution outperforms existing circular models in the case study.

## Abstract

The technique of wrapping of a univariate probability distribution is very effective in getting a circular form of the underlying density. In this article, we introduce the circular (wrapped) version of xgamma distribution and study its different distributional properties. To estimate the unknown parameter, maximum likelihood method is proposed. A Monte-Carlo simulation study is performed to understand the behaviour of the estimates for varying sample size. To illustrate the application of the proposed distribution, a real data set on the long axis orientation of feldspar laths in basalt rock is analyzed and compared with other circular distributions.