We study the behavior of exponential random graphs in both the sparse and the dense regime. We show that exponential random graphs are approximate mixtures of graphs with independent edges whose probability matrices are critical points of an associated functional, resulting in a matrix equation. In the dense regime, every solution to this equation is close to a block matrix, concluding that the...

 Abstract: A new method to generate various family of distributions is introduced. This method introduces a new two-parameter extension of the exponential distribution to illustrate its application. Some statistical and reliability properties of the new distribution, including explicit expressions for the moments, quantiles, mode, moment generating function, mean residual lifetime, stochas...

A new algorithm is developed for computing etAB, where A is an n× n matrix and B is n×n0 with n0 ≪ n. The algorithm works for any A, its computational cost is dominated by the formation of products of A with n× n0 matrices, and the only input parameter is a backward error tolerance. The algorithm can return a single matrix etAB or a sequence etkAB on an equally spaced grid of points tk. It uses...

Two approaches for closing the turbulence subgrid-scale stress tensor in terms of matrix exponentials are introduced and compared. The first approach is based on a formal solution of the stress transport equation in which the production terms can be integrated exactly in terms of matrix exponentials. This formal solution of the subgrid-scale stress transport equation is shown to be useful to ex...

This note summarizes various derivations, formulas and computational algorithms relevant to the Fisher information matrix of Gaussian graphical models with respect to either an exponential parameterization (related to the information form) or the corresponding moment parameterization. 1 Gauss-Markov Models The probability density of a Gaussian random vector x ∈ R may be expressed in information...

We extend previous results on the exponential off-diagonal decay of the entries of analytic functions of banded and sparse matrices to the case where the matrix entries are elements of a C∗-algebra.

Sinc-Galerkin method based upon double exponential transformation for solving Troesch's problem was given in this study. Properties of the Sinc-Galerkin approach were utilized to reduce the solution of nonlinear two-point boundary value problem to same nonlinear algebraic equations, also, the matrix form of the nonlinear algebraic equations was obtained.The error bound of the method was found. ...

The unified hybrid censoring is a mixture of generalized Type-I and Type-II hybrid censoring schemes. This article presents the statistical inferences on Generalized Exponential Distribution parameters when the data are obtained from the unified hybrid censoring scheme. It is observed that the maximum likelihood estimators can not be derived in closed form. The EM algorithm for computing the ma...

Small relative perturbations to the entries of an essentially nonnegative matrix introduce small relative errors to entries of its exponential. It is thus desirable to compute the exponential with high componentwise relative accuracy. Taylor series approximation coupled with scaling and squaring is used to compute the exponential of an essentially nonnegative matrix. An a priori componentwise r...