When an investlgator records an observation by nature according to a certain stochastic model the recorded observation will not have the original distribution unless everJ observation is given an equal chance of being recorded. A number of papers have appeared during the last ten years implicitly using the concepts of weighted and size-biased sampling distributions. In this paper we examine some general models leading to weighted distributiosls with weight functions not necessarily bounded by unity. The examples include. probability sampling in sasnple surveys additive damage models visibility bias dependent on the nature of data collection and two-stage sampling. Several important distributions and their size-biased fornls are recorded. A few theorems are given on the inequalities between the mean values of two weighted distributions. The results are applied to the analysis of data relating to human populations and wildlife management. For human populations the following is raised and discussed. Let us ascertain from each snale student in a class the nusHber of brothers including himself and sisters he has and denote by k the number of students and by B and S the total numbers of brothers and sisters. What would be the approximate values of B/(B + S) the ratio of brothers to the total number of children asld (B + S)/k the average number of children per family? It is shown that B/(B + S) will be an overestimate of the proportion of boys among the children per family in the general population which is about halB and similarly (B + S)/k is biased upwards as an estimate of the average number of children per family in the general population. Some suggestiosls are oJ%ered for the estimation of these population parameters. Lastly for the purpose of estimating wildlife population density certain results are formulated within the framework of quadrat sasnpling involving visibility bias. fw(x) = w(x) f(x) (1.1)

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Symbolic dynamic filtering (SDF) has been recently reported in literature as a pattern recognition tool for early detection of anomalies (i.e., deviations from the nominal behavior) in complex dynamical systems. This paper presents a review of SDF and its performance evaluation relative to other classes of pattern recognition tools, such as Bayesian Filters and Artificial Neural Networks, from the perspectives of: (i) anomaly detection capability, (ii) decision making for failure mitigation and (iii) computational efficiency. The evaluation is based on analysis of time series data generated from a nonlinear active electronic system.

Two objects with homologous landmarks are said to be of the same shape if the configurations of landmarks of one object can be exactly matched with that of the other by translation, rotation/reflection, and scaling. The observations on an object are coordinates of its landmarks with reference to a set of orthogonal coordinate axes in an appropriate dimensional space. The origin, choice of units, and orientation of the coordinate axes with respect to an object may be different from object to object. In such a case, how do we quantify the shape ofan object, find the mean and variation of shape in a population of objects, compare the mean shapes in two or more different populations, and discriminate between objects belonging to two or more different shape distributions. We develop some methods that are invariant to translation, rotation, and scaling of the observations on each object and thereby provide generalizations of multivariate methods for shape analysis.