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with two parameters, a (location) and b > 0 (scale), [2, p. 50]. The Cauchy distribution occurs in numerous applications, see, e.g., [3, p. 159]. A recent interest in C(a, b) is due to its “fat tails”, accounting for outliers (rare events) better than the more concentrated distributions commonly used, in particular the normal distribution. Indeed, these “rare” events with significant consequenc...

It is shown that the sample paths of Poisson shot noise with heavy-tailed semiexponential distributions satisfy a large deviation principle with a rate function that is insensitive to the shot shape. This demonstrates that, on the scale of large deviations, paths to rare events do not depend on the shot shape.

In many real world applications, systematic analysis of rare events, such as credit card frauds and adverse drug reactions, is very important. Their low occurrence rate in large databases often makes it difficult to identify the risk factors from straightforward application of associations and sequential pattern discovery. In this paper we introduce a heuristic to guide the search for interesti...

Suppose that the integers are assigned i.i.d. random variables f! x g (taking values in the unit interval), which serve as an environment. This environment deenes a random walk fX n g (called a RWRE) which, when at x, moves one step to the right with probability ! x , and one step to the left with probability 1 ? ! x. Solomon (1975) determined the almost-sure asymptotic speed v (=rate of escape...

The dynamical evolution of many economic, sociological, biological and physical systems tends to be dominated by a relatively small number of unexpected, large changes ('extreme events'). We study the large, internal changes produced in a generic multi-agent population competing for a limited resource, and find that the level of predictability actually increases prior to a large change. These l...

Pilomatricoma or benign calcifying epithelioma of Malherbe is a benign appendageal tumour originating from primitive cells of the hair matrix. Perforation (transepidermal elimination), bullous or anetodermic cutaneous changes overlying pilomatricomas are rare events. In this report, we describe a case of pilomatricoma with bullous appearance or secondary anetoderma. The tumour was totally excis...

Let (Xn,i )1≤i≤n,n∈N be a triangular array of row-wise stationary Rd valued random variables. We use a “blocks method” to define clusters of extreme values: the rows of (Xn,i ) are divided into mn blocks (Yn,j ), and if a block contains at least one extreme value, the block is considered to contain a cluster. The cluster starts at the first extreme value in the block and ends at the last one. T...

High-value rare-event searching is arguably the most natural application of grid computing, where computational tasks are distributed to a large collection of clients (which comprise the computation grid) in such a way that clients are rewarded for performing tasks assigned to them. Although natural, rare-event searching presents significant challenges for a computation supervisor, who partitio...

Statistical NLP inevitably deals with a large number of rare events As a consequence NLP data often vio lates the assumptions implicit in traditional statistical procedures such as signi cance testing We describe a signi cance test an exact conditional test that is appropriate for NLP data and can be performed us ing freely available software We apply this test to the study of lexical relations...