Parameter Models and Estimators of Fiber and Cluster Processes

Jan-Olof Johansson and Ola Hössjer

Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,

ISSN 1403-9338
We present general parametric models for fiber and cluster processes. These models can be used in several technical and natural applications and we have applied the fiber model to the micro-structure of paper. In that application we have generalized earlier models and suggested a new distribution for the fiber directions.
A least square estimator of the model covariance function and a Maximum Likelihood estimator are introduced. In the paper application, the least square estimator of the covariance function have been used to estimate the model parameters, which include the fiber geometry and the intensity of the fibers.
Key words:
Fiber process, cluster process, covariance function, variogram, estimation.