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A completely new approach to the problem of energy distribution in statistical mechanics is developed that results in a general, combinatorial formula for the density of states. Relying on the approach the energy equipartition principle is…
Exponential family distributions are highly useful in machine learning since their calculation can be performed efficiently through natural parameters. The exponential family has recently been extended to the t-exponential family, which…
Several applications require spatial distributions of the incident electric field that maximize the electric field at a focal point for a given input power. The field distributions are derived for various optical systems in a direct way…
We develop a general method for power spectrum analysis of three dimensional redshift surveys. We present rigorous analytical estimates for the statistical uncertainty in the power and we are able to derive a rigorous optimal weighting…
Probability distributions which emerge from the formalism of nonextensive statistical mechanics have been applied to a variety of problems. In this paper we unite modeling of such distributions with the model of widespread 1/f noise. We…
The distribution of impact factors has been modeled in the recent informetric literature using two-exponent law proposed by Mansilla et al. (2007). This paper shows that two distributions widely-used in economics, namely the Dagum and…
The piecewise exponential model is a flexible non-parametric approach for time-to-event data, but extrapolation beyond final observation times typically relies on random walk priors and deterministic knot locations, resulting in unrealistic…
The aim of this paper is to extend Azzalini's method. This extension is done in two stages: consider two dependent and non-identically distributed random variables say $X_1$ and $X_2$; model the dependence between $X_1$ and $X_2$ by a…
Power System State Estimation (PSSE) has been a research area of interest for power engineers for a long period of time. Due to the intermittent nature of renewable energy sources, which are applied in the power network more than before,…
We introduce a new broad and exible class of multivariate elliptically symmetric distributions in- cluding the elliptically symmetric logistic and multivariate normal. Various probabilistic properties of the new distribution are studied,…
We transformed the generalized exponential power series to another functional form suitable for further analysis. By applying the Cauchy-Euler differential operator in the form of an exponential operator, the series became a sum of…
Distribution system end users are transforming from passive to active participants, marked by the push towards widespread adoption of edge-level Distributed Energy Resources (DERs). This paper addresses the challenges in distribution system…
In this article, we propose a new three parameter distribution by compounding negative binomial with reciprocal inverse Gaussian model called negative binomial-reciprocal inverse Gaussian distribution. This model is tractable with some…
This paper is devoted to study a new three- parameters model called the Exponential Flexible Weibull extension (EFWE) distribution which exhibits bathtub-shaped hazard rate. Some of it's statistical properties are obtained including…
We consider the problem of reconstructing the dynamic state matrix of transmission power grids from time-stamped PMU measurements in the regime of ambient fluctuations. Using a maximum likelihood based approach, we construct a family of…
Probability distributions of money, income, and energy consumption per capita are studied for ensembles of economic agents. The principle of entropy maximization for partitioning of a limited resource gives exponential distributions for the…
We propose a class of structured diffusion models, in which the prior distribution is chosen as a mixture of Gaussians, rather than a standard Gaussian distribution. The specific mixed Gaussian distribution, as prior, can be chosen to…
We introduce a class of distributions originating from an exponential family and having a property related to the strict stability property. A characteristic function representation for this family is obtained and its properties are…
In this paper we develop a bivariate discrete generalized exponential distribution, whose marginals are discrete generalized exponential distribution as proposed by Nekoukhou, Alamatsaz and Bidram ("Discrete generalized exponential…