Survival analysis in Johnson–Mehl Tessellation

The crystallization process is represented here by a generalized Boolean model, whose parameters are usually unknown. A better understanding of the model may be obtained if we estimate the corresponding parameters. In this paper, we provide non-parametric estimators for the parameters of the model. Among them, the degree of crystallinity at time t is the probability that an arbitrary point in the space has been captured by a crystal before time t. We estimate it following the Kaplan–Meier approach extended to the context of a Johnson–Mehl incomplete tessellation. Three estimators are defined, according to the kind of data we dispose. The results are also illustrated by simulations. We also provide estimators for the parameters describing geometrical aspects of the phenomenon.