Related papers: Zero-Class Poisson for Rare-Event Studies
The Poisson process is one of the simplest stochastic processes defined in continuous time, having interesting mathematical properties, leading, in many situations, to applications mathematically treatable. One of the limitations of the…
Accurate modeling is essential in integer-valued real phenomena, including the distribution of entire data, zero-inflated (ZI) data, and discrete exceedances. The Poisson and Negative Binomial distributions, along with their ZI variants,…
Inspired by the recent proposal by Feldman and Cousins of a ``unified approach to the classical statistical analysis of small signals'' based on a choice of ordering in Neyman's construction of classical confidence intervals, I propose a…
Competing and Complementary risk (CCR) problems are often modelled using a class of distributions of the maximum, or minimum, of a random number of i.i.d. random variables; we call this class the CCR class of distributions. While the CCR…
Based on recent findings by Bourguin and Peccati, we give a fourth moment type condition for an element of a free Poisson chaos of arbitrary order to converge to a free (centered) Poisson distribution. We also show that free Poisson chaos…
The polynomial birth-death distribution (abbr. as PBD) on $\ci=\{0,1,2, >...\}$ or $\ci=\{0,1,2, ..., m\}$ for some finite $m$ introduced in Brown & Xia (2001) is the equilibrium distribution of the birth-death process with birth rates…
The EMCCD is a CCD type that delivers fast readout and negligible detector noise, making it an ideal detector for high frame rate applications. Because of the very low detector noise, this detector can potentially count single photons.…
Dictionary learning methods continue to gain popularity for the solution of challenging inverse problems. In the dictionary learning approach, the computational forward model is replaced by a large dictionary of possible outcomes, and the…
Current Zero-Shot Learning (ZSL) approaches are restricted to recognition of a single dominant unseen object category in a test image. We hypothesize that this setting is ill-suited for real-world applications where unseen objects appear…
Clustering is a crucial task in various domains of knowledge, including medicine, epidemiology, genomics, environmental science, economics, and visual sciences, among others. Methodologies for inferring the number of clusters have often…
We introduce a new class of Poisson-exponential-Tweedie (PET) mixture in the framework of generalized linear models for ultra-overdispersed count data. The mean-variance relationship is of the form $m+m^{2}+\phi m^{p}$, where $\phi$ and $p$…
The (conditional or unconditional) distribution of the continuous scan statistic in a one-dimensional Poisson process may be approximated by that of a discrete analogue via time discretization (to be referred to as the discrete…
In this paper we study the identification of an event region $X$ within a larger region $Y$, in which the sensors are distributed by a Poisson process of density $\lambda$ to detect this event region, i.e., its boundary. The model of sensor…
Two new information-theoretic methods are introduced for establishing Poisson approximation inequalities. First, using only elementary information-theoretic techniques it is shown that, when $S_n=\sum_{i=1}^nX_i$ is the sum of the (possibly…
There are numerous applications which involve modeling multi-dimensional count data, notably in actuarial science and risk management. When such data exhibit an excess of zeros, common count models are no longer suitable. With multivariate…
Poisson-like behavior for event count data is ubiquitous in nature. At the same time, differencing of such counts arises in the course of data processing in a variety of areas of application. As a result, the Skellam distribution -- defined…
Few-shot and zero-shot text classification aim to recognize samples from novel classes with limited labeled samples or no labeled samples at all. While prevailing methods have shown promising performance via transferring knowledge from seen…
We study the general problem of testing whether an unknown distribution belongs to a specified family of distributions. More specifically, given a distribution family $\mathcal{P}$ and sample access to an unknown discrete distribution…
We prove a dichotomy for Manneville-Pomeau maps $f:[0,1]\to [0, 1]$: given any point $\zeta\in [0,1]$, either the Rare Events Point Processes (REPP), counting the number of exceedances, which correspond to entrances in balls around $\zeta$,…
Methods have been developed to identify the probability distribution of a random vector $Z$ from information consisting of its bounded range and the probability density function or moments of a quantity of interest, $Q(Z)$. The mapping from…