相关论文: Dispersion measure for symmetric, stable probabili…

Stochastic diffusion equations are crucial for modeling a range of physical phenomena influenced by uncertainties. We introduce the generalized finite difference method for solving these equations. Then, we examine its consistency,…

We derive a simple and precise approximation to probability density functions in sampling distributions based on the Fourier cosine series. After clarifying the required conditions, we illustrate the approximation on two examples: the…

We present a new uncertainty principle for risk-aware statistical estimation, effectively quantifying the inherent trade-off between mean squared error ($\mse$) and risk, the latter measured by the associated average predictive squared…

For certain types of statistical models, the characteristic function (Fourier transform) is available in closed form, whereas the probability density function has an intractable form, typically as an infinite sum of probability weighted…

Predicting extreme events is important in many applications in risk analysis. The extreme-value theory suggests modelling extremes by max-stable distributions. The Bayesian approach provides a natural framework for statistical prediction.…

Circular variables that represent directions or periodic observations arise in many fields, such as biology and environmental sciences. An important issue when dealing with circular data is how to estimate their dispersion robustly,…

We derive a large deviation principle for families of random variables in the basin of attraction of spectrally positive stable distributions by proving a uniform version of the Tauberian theorem for Laplace-Stieltjes transforms. The main…

Techniques from numerical bifurcation theory are very useful to study transitions between steady fluid flow patterns and the instabilities involved. Here, we provide computational methodology to use parameter continuation in determining…

For every discrete or continuous location-scale family having a square-integrable density, there is a unique continuous probability distribution on the unit interval that is determined by the density-quantile composition introduced by…

A statistical mechanics theory for a fluid stratified in density is presented. The predicted statistical equilibrium state is the most probable outcome of turbulent stirring. The slow temporal evolution of the vertical density profile is…

A new distribution named intensive natural distribution is introduced with the intent of consolidating statistics and empirical data. Based on the probability derived from the Bernoulli distribution, this method extended also Poisson…

We investigate the diffusive properties of energy fluctuations in a one-dimensional diatomic chain of hard-point particles interacting through a square--well potential. The evolution of initially localized infinitesimal and finite…

Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either the first time derivative or the second space derivative by a derivative of fractional order. The fundamental solutions of…

We propose a method to infer the presence and location of change-points in the distribution of a sequence of independent data taking values in a general metric space, where change-points are viewed as locations at which the distribution of…

The Baxter permuton is a random probability measure on the unit square which describes the scaling limit of uniform Baxter permutations. We find an explict formula for the expectation of the Baxter permuton, i.e.\ the density of its…

The two-parameter distribution known as exponential-Poisson (EP) distribution, which has decreasing failure rate, was introduced by Kus (2007). In this paper we generalize the EP distribution and show that the failure rate of the new…

We present a computational framework to investigate steady state distributions and perform stability analysis for random ordinary differential equations driven by parameter uncertainty. Using the nonlinear Rosenzweig McArthur predator prey…

In dissipative dynamical systems phase space volumes contract, on average. Therefore, the invariant measure on the attractor is singular with respect to the Lebesgue measure. As noted by Ruelle, a generic perturbation pushes the state out…

This work aims to assess how well a model performs under distribution shifts without using labels. While recent methods study prediction confidence, this work reports prediction dispersity is another informative cue. Confidence reflects…

We propose a simpler derivation of the probability density function of Feller Diffusion using the Fourier Transform and solving the resulting equation via the Method of Characteristics. We also discuss simulation algorithms and confirm key…