Related papers: Extended Poisson-Tweedie: properties and regressio…
Diffusion models have emerged as powerful tools for solving inverse problems, yet prior work has primarily focused on observations with Gaussian measurement noise, restricting their use in real-world scenarios. This limitation persists due…
Tweedie's formula is central to measurement-error analysis and empirical Bayes. Under Gaussian noise, the formula identifies the posterior mean directly from the observed-data density, bypassing nonparametric deconvolution. Beyond a few…
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…
Many of the data, particularly in medicine and disease mapping are count. Indeed, the under or overdispersion problem in count data distrusts the performance of the classical Poisson model. For taking into account this problem, in this…
Conway-Maxwell-Poisson (CMP) distributions are flexible generalizations of the Poisson distribution for modelling overdispersed or underdispersed counts. The main hindrance to their wider use in practice seems to be the inability to…
The analysis of count data is commonly done using Poisson models. Negative binomial models are a straightforward and readily motivated generalization for the case of overdispersed data, i.e., when the observed variance is greater than…
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,…
Bivariate count models having one marginal and the other conditionals being of the Poissons form are called pseudo-Poisson distributions. Such models have simple exible dependence structures, possess fast computation algorithms and generate…
Researchers are often interested in understanding the relationship between a set of covariates and a set of response variables. To achieve this goal, the use of regression analysis, either linear or generalized linear models, is largely…
The negative binomial distribution has been widely used as a more flexible model than the Poisson distribution for count data. However, when the true data-generating process is Poisson, it is often challenging to distinguish it from a…
Data on count processes arise in a variety of applications, including longitudinal, spatial and imaging studies measuring count responses. The literature on statistical models for dependent count data is dominated by models built from…
This paper presents a new method to estimate systematic errors in the maximum-likelihood regression of count data. The method is applicable in particular to X-ray spectra in situations where the Poisson log-likelihood, or the Cash…
Compound Poisson distributions have been employed by many authors to fit experimental data, typically via the method of moments or maximum likelihood estimation. We propose a new technique and apply it to several sets of published data. It…
Tweedie exponential dispersion family constitutes a fairly rich sub-class of the celebrated exponential family. In particular, a member, compound Poisson gamma (CP-g) model has seen extensive use over the past decade for modeling mixed…
Count data take on non-negative integer values and are challenging to properly analyze using standard linear-Gaussian methods such as linear regression and principal components analysis. Generalized linear models enable direct modeling of…
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…
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…
A general random effects model is proposed that allows for continuous as well as discrete distributions of the responses. Responses can be unrestricted continuous, bounded continuous, binary, ordered categorical or given in the form of…
The problem of subgroups is ubiquitous in scientific research (ex. disease heterogeneity, spatial distributions in ecology...), and piecewise regression is one way to deal with this phenomenon. Morse-Smale regression offers a way to…
In this paper, we present a method for factor analysis of discrete data. This is accomplished by fitting a dependent Poisson model with a factor structure. To be able to analyze ordinal data, we also consider a truncated Poisson…