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Exponential random graph models have attracted significant research attention over the past decades. These models are maximum-entropy ensembles under the constraints that the expected values of a set of graph observables are equal to given…
Neural posterior estimation (NPE), a simulation-based computational approach for Bayesian inference, has shown great success in approximating complex posterior distributions. Existing NPE methods typically rely on normalizing flows, which…
We introduce a class of two-parameter discrete dispersion models, obtained by combining convolution with a factorial tilting operation, similar to exponential dispersion models which combine convolution and exponential tilting. The…
In this paper, an alternative mixed Poisson distribution is proposed by amalgamating Poisson distribution and a modification of the Quasi Lindley distribution. Some fundamental structural properties of the new distribution, namely the shape…
In this paper, we introduce a new bivariate distribution we called it bivariate expo- nentiated modified Weibull extension distribution (BEMWE). The model introduced here is of Marshall-Olkin type. The marginals of the new bivariate…
Suppose that the distribution of $X_a$ belongs to a natural exponential family concentrated on the nonegative integers and is such that $\E(z^{X_a})=f(az)/f(a)$. Assume that $\Pr(X_a\leq k)$ has the form $c_k\int_a ^{\infty}u^k\mu(du)$ for…
In various practical situations, we encounter data from stochastic processes which can be efficiently modelled by an appropriate parametric model for subsequent statistical analyses. Unfortunately, the most common estimation and inference…
Two-component mixture models are particularly useful for identifying differentially expressed genes, but their performance can deteriorate markedly when the alternative distribution departs from parametric assumptions or symmetry. We…
Often we consider machine learning models or statistical analysis methods which we endeavour to alter, by introducing a randomized mechanism, to make the model conform to a differential privacy constraint. However, certain models can often…
Commonly observed patterns typically follow a few distinct families of probability distributions. Over one hundred years ago, Karl Pearson provided a systematic derivation and classification of the common continuous distributions. His…
In this paper we study a wide and flexible family of discrete distributions, the so-called generalized negative binomial (GNB) distributions that are mixed Poisson distributions in which the mixing laws belong to the class of generalized…
We present a consistent method to calculate the probability distribution of soliton parameters in systems with additive noise. Even though a weak noise is considered, we are interested in probabilities of large fluctuations (generally…
In this letter, we give a concise, closed-form expression for the differential entropy of the sum of two independent, non-identically-distributed exponential random variables. The derivation is straightforward, but such a concise entropy…
A numerical method is proposed to evaluate the survival function of a compound distribution and the stop-loss premiums associated with a non-proportional global reinsurance treaty. The method relies on a representation of the probability…
We develop differentially private methods for estimating various distributional properties. Given a sample from a discrete distribution $p$, some functional $f$, and accuracy and privacy parameters $\alpha$ and $\varepsilon$, the goal is to…
The analysis of Tables of particle properties shows that the probability distribution of the results of physical measurements is far from the conventional Gaussian $\rho(\xi)=exp(-\xi^2/2) $, but is more likely to follow the simple…
This paper investigates score-based diffusion models when the underlying target distribution is concentrated on or near low-dimensional manifolds within the higher-dimensional space in which they formally reside, a common characteristic of…
To account quantitatively for many reported ``natural'' fat tail distributions in Nature and Economy, we propose the stretched exponential family as a complement to the often used power law distributions. It has many advantages, among which…
In this paper, we introduce a family of discrete rectangular uniform distributions on the natural numbers-referred to as orthogonal dice-characterized by the property that their means equal their variances. These distributions arise…
In their fundamental paper on cubic variance functions, Letac and Mora (The Annals of Statistics,1990) presented a systematic, rigorous and comprehensive study of natural exponential families on the real line, their characterization through…