The amount of data produced by molecular biologists is growing at an exponential rate. Some of the fastest growing sets of data are measurements of gene expression, comparable in quantity only to gene sequences and the vast biological literature. Both gene expression data and sequence data offer hints as to the functions of thousands of newly discovered genes, but neither give complete answers....

An algorithm is presented which, for a large-dimensional exponential family G, nds a lower dimension exponential sub-family of G which contains distributions best tting groups of identically distributed observations within a set of data. The data are therefore tted to a family of distributions which has been adaptively chosen as representative of them. The algorithm is implemented in the specia...

This article introduces a new family of Generalized Exponentiated Exponential distribution. Using the T-R{Y} framework, T-Exponentiated Exponential{Y} distributions named Exponential{Frechet} is proposed. Some general properties such as hazard rate function, quantile non-central moment, mode, mean absolute deviations and Shannon’s entropy are discussed. A continuous univariate probability distr...

We study the problem of finding the smallest m such that every element of an exponential family can be written as a mixture of m elements of another exponential family. We propose an approach based on coverings and packings of the face lattice of the corresponding convex support polytopes and results from coding theory. We show that m = qN−1 is the smallest number for which any distribution of ...

We demonstrate that the q-exponential family particularly admits natural geometrical structures among deformed exponential families. The property is the invariance of structures with respect to a general linear group, which transitively acts on the space of positive definite matrices. We prove this property via the correspondence between information geometry induced by a deformed potential on t...

Motivated by a recent result by van Erven and Harremoës, we study a forward projection problem for the Rényi divergence on a particular α-convex set, termed αlinear family. The solution to this problem yields a parametric family of probability measures which turns out to be an extension of the exponential family, and it is termed αexponential family. An orthogonality relationship between the αe...