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Expectation Propagation is a very popular algorithm for variational inference, but comes with few theoretical guarantees. In this article, we prove that the approximation errors made by EP can be bounded. Our bounds have an asymptotic…
Negation operation is important in intelligent information processing. Different with existing arithmetic negation, an exponential negation is presented in this paper. The new negation can be seen as a kind of geometry negation. Some basic…
We show that size-rank distributions with power-law decay (often only over a limited extent) observed in a vast number of instances in a widespread family of systems obey Tsallis statistics. The theoretical framework for these distributions…
This paper introduces a new four-parameter lifetime model called the Weibull Birnbaum-Saunders distribution. This new distribution represents a more flexible model for the lifetime data. Its failure rate function can be increasing,…
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…
We derive an efficient method to calculate exceedance probabilities (EP) for the Dirichlet distribution when the number of event types is larger than two. Also, we present an intuitive application of Dirichlet EPs and compare our method to…
This paper considers the robust and efficient implementation of Gaussian process regression with a Student-t observation model. The challenge with the Student-t model is the analytically intractable inference which is why several…
In this paper the generalization of the Poisson distribution is derived for the case when each consecutive event changes event rate. A simple formula for the probability of observing of a given number of events for the selected period of…
Explosive percolation (EP) has received significant research attention due to its rich and anomalous phenomena near criticality. In our recent study [Phys. Rev. Lett. 130, 147101 (2023)], we demonstrated that the correct critical behaviors…
In this communication, we introduce a new statistical model and study its various mathematical properties. The expressions for hazard rate, reversed hazard rate, and odd functions are provided. We explore the asymptotic behaviors of the…
The Conway-Maxwell-Poisson distribution is a two-parameter generalisation of the Poisson distribution that can be used to model data that is under- or over-dispersed relative to the Poisson distribution. The normalizing constant…
We study nonparametric estimation of the distribution function (DF) of a continuous random variable based on a ranked set sampling design using the exponentially tilted (ET) empirical likelihood method. We propose ET estimators of the DF…
This paper describes the Elliptical Quartic Exponential distribution in $\mathbb{R}^D$, obtained via a maximum entropy construction by imposing second and fourth moment constraints. I discuss relationships to related work, analytical…
We present a general theory of spontaneous emission at exceptional points (EPs)---exotic degeneracies in non-Hermitian systems. Our theory extends beyond spontaneous emission to any light--matter interaction described by the local density…
A consistent generalization of statistical mechanics is obtained by applying the maximum entropy principle to a trace-form entropy and by requiring that physically motivated mathematical properties are preserved. The emerging…
In this paper, we introduce a bivariate exponentaited generalized Weibull-Gompertz distribution. The model introduced here is of Marshall-Olkin type. Several properties are studied such as bivariate probability density function and it is…
In this paper, we consider the problem of parameter estimating for a family of exponential distributions. We develop the improved estimation method, which generalized the James--Stein approach for a wide class of distributions. The proposed…
Exponential random graph models are an important tool in the statistical analysis of data. However, Bayesian parameter estimation for these models is extremely challenging, since evaluation of the posterior distribution typically involves…
A new class of distributions based on phase-type distributions is introduced in the current paper to model lifetime data in the field of reliability analysis. This one is the natural extension of the distribution proposed by Acal et al.…
We consider a family of infinite dimensional product measures with tails between Gaussian and exponential, which we call $p$-exponential measures. We study their measure-theoretic properties and in particular their concentration. Our…