Speakers
- Professor Dietrich Stoyan — TU Bergakademie Freiberg
Abstract
In the context of statistics for oversize particles appearing in comminution processes,
the idea arose of using point process methods. The mathematical model for this approach
is the marked point process: This is a random set of points $x_i$ on the positive real
line, each with a mark $m_i$. Here, the $x_i$ represent particle sizes and the $m_i$
represent particle volumes, sizes, or shape characteristics.
A main reason for this approach is that a sample of particles is often not a mathematical
sample of independent, identically distributed objects of a fixed number $n$, but rather
a random set of particles, such as sugar crystals in a spoon, of a random number and with
possible correlations of sizes and shapes. Therefore, classical mathematical statistics
should not be used.
Rather than using particle size distributions, which always require normalisation,
intensity functions can be used. This circumvents problems that arise when fine particles appear
in large numbers. The point-process approach simplifies calculations, paves the way for
new models and provides mathematical proofs of well-known formulas for particle statistics,
as detailed in the classic book by Allen (2003).
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