A family of generalized Cauchy distributions, T-Cauchy{Y} family, is proposed using the T-R{Y} framework. The family of distributions is generated using the quantile functions of uniform, exponential, log-logistic, logistic, extreme value, and Fréchet distributions. Several general properties of the T-Cauchy{Y} family are studied in detail including moments, mean deviations and Shannon’s entrop...

Mayr and Meyer [MM] found ideals with the doubly exponential ideal membership property. Further investigations of the doubly exponential properties of these ideals can be found in Bayer and Stillman [BS], Demazure [D], and Koh [K]. Following a question of Bayer, Huneke and Stillman, the author has investigated in [S1, S2, S3] the properties of the primary decompositions and the associated prime...

This work considers the problem of learning the underlying statistical structure of multidimensional data of mixed probability distribution types (continuous and discrete) for the purpose of fitting a generative model and making decisions in a data-driven manner. Using properties of exponential family distributions and generalizing classical linear statistics techniques, a unified theoretical m...

We present a new class of statistical models, designed for life history analysis of plants and animals, that allow joint analysis of data on survival and reproduction over multiple years, allow for variables having different probability distributions, and correctly account for the dependence of variables on earlier variables. We illustrate their utility with an analysis of data taken from an ex...

In this paper, we study Amari’s natural gradient flows of real functions defined on the densities belonging to an exponential family on a finite sample space. Our main example is the minimization of the expected value of a real function defined on the sample space. In such a case, the natural gradient flow converges to densities with reduced support that belong to the border of the exponential ...