Strictly operator-stable distributions

Estimating Strictly Piecewise Distributions

Strictly Piecewise (SP) languages are a subclass of regular languages which encode certain kinds of long-distance dependencies that are found in natural languages. Like the classes in the Chomsky and Subregular hierarchies, there are many independently converging characterizations of the SP class (Rogers et al., to appear). Here we define SP distributions and show that they can be efficiently e...

Strictly Semi-transitive Operator Algebras

An algebra A of operators on a Banach space X is called strictly semitransitive if for all non-zero x, y ∈ X there exists an operator A ∈ A such that Ax = y or Ay = x. We show that if A is norm-closed and strictly semi-transitive, then every A-invariant linear subspace is norm-closed. Moreover, LatA is totally and well ordered by reverse inclusion. If X is complex and A is transitive and strict...

Estimation for Strictly Positive Stable Laws

Positive stable laws have become a standard tool in modelling heavy tailed data in such diverse areas as finance, engineering and survival analysis. Due to the non–existence of closed–form expression for the corresponding densities, standard procedures for estimation of the parameters of positive stable distributions appear to be computationally expensive. In this note we show that the first tw...

Stable Distributions

Stable Distributions

We give some explicit calculations for stable distributions and convergence to them, mainly based on less explicit results in Feller [3]. The main purpose is to provide ourselves with easy reference to explicit formulas and examples. (There are probably no new results.)