Title: Planar segment processes with reference mark distributions, modeling and estimation,
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.