# Planar segment processes with reference mark distributions, modeling and estimation

## TL;DR

This paper introduces statistical methods for modeling planar segment processes with reference distributions, combining parametric and non-parametric estimation techniques, and demonstrates their effectiveness through simulation studies.

## Contribution

It develops a general theoretical framework and two specific models for segment processes with reference distributions, including estimation procedures and simulation validation.

## Key findings

- Estimation methods effectively recover reference distributions.
- Simulation studies show estimators' variability and accuracy.
- Models accommodate inhomogeneous and Gibbs-type segment processes.

## Abstract

The paper deals with planar segment processes given by a density with respect to the Poisson process. Parametric models involve reference distributions of directions and/or lengths of segments. These distributions generally do not coincide with the corresponding observed distributions. Statistical methods are presented which first estimate scalar parameters by known approaches and then the reference distribution is estimated non-parametrically. Besides a general theory we offer two models, first a Gibbs type segment process with reference directional distribution and secondly an inhomogeneous process with reference length distribution. The estimation is demonstrated in simulation studies where the variability of estimators is presented graphically.