Stochastic order relations prprovide a valuable insight into the behaviour of complex stochastic (random) systems and enable the user to collect meaningful comparative data. Application areas include queueing systems, actuarial and financial risk, decision making and stochastic simulation. Applicable to a broad range of scientific disciplines, including economics, finance, insurance and operations research Provides coverage of the latest research and applications An essential resource for researchers and postgraduate students appliying stochastic order relations, and scientisits from applied statistics, operations research, economics and finance.

This monograph on the results and methods of stochastic geometry and spatial statistics is accessible to practitioners and non-theoreticians, and may also be used as an introduction to the subject. Topics covered include the basic theories of point processes, random sets, fibre and surface processes, random tessellations, stereology and the statistical theory of shape. The theory is illustrated by many examples drawn from different branches of science; actual data in the form of images are presented, and their statistical analyses are discussed.

In Part I the reader is introduced to the methods of measuring the fractal dimension of irregular geometric structures. Part II demonstrates important modern methods for the statistical analysis of random shapes. The statistical theory of point fields, with and without marks, is introduced in Part III. Each of the three sections concentrates on the mathematical ideas, rather than detailed proofs, and can be read independently.