Related papers: A tutorial on Palm distributions for spatial point…
In this work we define the plasma dispersion function for a suprathermal plasma described with a regularized kappa distribution. As is known from Maxwellian as well as (standard) kappa plasmas, the respective Fried-Conte and the modified…
A method is given for calculation of a distribution of small particles, embedded in a medium, so that the resulting medium would have a desired radiation pattern for the plane wave scattering by this medium.
Spatio-temporal point processes (STPPs) model discrete events distributed in time and space, with important applications in areas such as criminology, seismology, epidemiology, and social networks. Traditional models often rely on…
Prompted by modern technologies in data acquisition, the statistical analysis of spatially distributed function-valued quantities has attracted a lot of attention in recent years. In particular, combinations of functional variables and…
A method is presented for finding anisotropic distribution functions for stellar systems with known, spherically symmetric, densities, which depends only on the two classical integrals of the energy and the magnitude of the angular…
We give several applications of the thick distributional calculus. We consider homogeneous distributions, point source fields, and higher order derivatives of order $0.$
In this work, we propose FastDPM, a unified framework for fast sampling in diffusion probabilistic models. FastDPM generalizes previous methods and gives rise to new algorithms with improved sample quality. We systematically investigate the…
Spatial Poisson point processes on finite-dimensional Euclidean space provide fundamental mathematical tools for modeling random spatial point patterns. In this paper, we introduce and analyze several Poisson-type spatial point processes.…
Diffusion models form an important class of generative models today, accounting for much of the state of the art in cutting edge AI research. While numerous extensions beyond image and video generation exist, few of such approaches address…
This paper develops methodology for local sensitivity analysis based on directional derivatives associated with spatial processes. Formal gradient analysis for spatial processes was elaborated in previous papers, focusing on distribution…
The mollified uniform distribution is rediscovered, which constitutes a ``soft'' version of the continuous uniform distribution. Important stochastic properties are presented and used to demonstrate potential fields of applications. For…
This paper introduces to readers the new concept and methodology of confidence distribution and the modern-day distributional inference in statistics. This discussion should be of interest to people who would like to go into the depth of…
A stochastic model is presented for a super-position of uncorrelated pulses with a random distribution of amplitudes, sizes, velocities and arrival times. The pulses are assumed to move radially with fixed shape and amplitudes decaying…
A new method for the statistical analysis of 3D point processes, based on the family of Minkowski functionals, is explained and applied to modelled galaxy distributions generated by a toy-model and cosmological simulations of the…
We derive an exact expression for the probability density function of the cascade size (total progeny) in a continuous state branching process when the generations are Gamma distributed. The distribution has application in the modelling of…
In distributional or average-case analysis, the goal is to design an algorithm with good-on-average performance with respect to a specific probability distribution. Distributional analysis can be useful for the study of general-purpose…
We consider the Busemann process in planar directed first passage percolation. We extend existing techniques to establish the existence of the process in our setting and determine its distribution in a number of integrable models. As…
I describe three ways that the spatial properties of a wave propagation medium can cause dispersion, and propose that they should form the basics for correctly understanding and naming phenomena described as "spatial dispersion". In…
Tempered stable distributions are frequently used in financial applications (e.g., for option pricing) in which the tails of stable distributions would be too heavy. Given the non-explicit form of the probability density function,…
We give the new distribution named Gamma Lindley distribution (GaLD), of which the Lindley distribution (LD) is a particular case. In this paper, we discuss and add more properties. Also, an application of this distribution is given.