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The problem of outliers is one of the oldest in statistics, and during the last century and a half interest in it has waxed and waned several times. Currently it is once again an active research area after some years of relative neglect, and recent work has solved a number of old problems in outlier theory, and identified new ones.

Each element is a member of one and only one class, and we shall mainly be concerned with populations with a large number of classes.

This monograph surveys the present state of Monte Carlo methods. For the sake of completeness, we cast a very brief glance in Chapter 4 at the direct simulation used in industrial and operational research, where the very simplest Monte Carlo techniques are usually sufficient.

Finite mixture distributions arise in a variety of applications ranging from the length distribution of fish to the content of DNA in the nuclei of liver cells. 1 Introduction This monograph is concerned with statistical distributions which can be expressed as superpositions of (usually simpler) component distributions.

Population genetics is the mathematical investigation of the changes in the genetic structure of populations brought about by selection, mutation, inbreeding, migration, and other phenomena, together with those random changes deriving from chance events.

The type of system we are interested in is a discrete-time or sampled-data system where the relation between input and output is (at least approximately) linear and where additive random dis turbances are also present, so that the behaviour of the system must be investigated by statistical methods.

Latent variable models are used in many areas of the social and behavioural sciences, and the increasing availability of computer packages for fitting such models is likely to increase their popularity.

The theory of risk already has its traditions. Further, non-life insurance, to which risk theory has, in fact, its most rewarding applications, was mainly outside the field of interest of the risk theorists.