相关论文: The Gamma-count distribution in the analysis of ex…
In this paper, a new mixed Poisson distribution is introduced. This new distribution is obtained by utilizing mixing process, with Poisson distribution as mixed distribution and Transmuted Exponential distribution as mixing distribution.…
We propose a new class of discrete generalized linear models based on the class of Poisson-Tweedie factorial dispersion models with variance of the form $\mu + \phi\mu^p$, where $\mu$ is the mean, $\phi$ and $p$ are the dispersion and…
A new two-parameter discrete distribution, namely the PoiG distribution is derived by the convolution of a Poisson variate and an independently distributed geometric random variable. This distribution generalizes both the Poisson and…
Univariate regression models have rich literature for counting data. However, this is not the case for multivariate count data. Therefore, we present the Multivariate Generalized Linear Mixed Models framework that deals with a multivariate…
Non-Gaussian outcomes are often modeled using members of the so-called exponential family. Notorious members are the Bernoulli model for binary data, leading to logistic regression, and the Poisson model for count data, leading to Poisson…
Although models for count data with over-dispersion have been widely considered in the literature, models for under-dispersion -- the opposite phenomenon -- have received less attention as it is only relatively common in particular research…
Factor analysis for high-dimensional data is a canonical problem in statistics and has a wide range of applications. However, there is currently no factor model tailored to effectively analyze high-dimensional count responses with…
An unbinned statistical test on cluster-like deviations from Poisson processes for point process data is introduced, presented in the context of time variability analysis of astrophysical sources in count rate experiments. The measure of…
Marginalized models are in great demand by most researchers in the life sciences particularly in clinical trials, epidemiology, health-economics, surveys and many others since they allow generalization of inference to the entire population…
The Poisson distribution has been widely studied and used for modeling univariate count-valued data. Multivariate generalizations of the Poisson distribution that permit dependencies, however, have been far less popular. Yet, real-world…
This paper gives a review of concentration inequalities which are widely employed in non-asymptotical analyses of mathematical statistics in a wide range of settings, from distribution-free to distribution-dependent, from sub-Gaussian to…
Count data frequently arises in biomedical applications, such as the length of hospital stay. However, their discrete nature poses significant challenges for appropriately modeling conditional quantiles, which are crucial for understanding…
Count-weighted temporal networks often exhibit unequal dispersion in the edge weights, which cannot be fully explained by modelling observational heterogeneity through latent factors in the conditional mean. Therefore, we propose new…
Real count data time series often show the phenomenon of the underdispersion and overdispersion. In this paper, we develop two extensions of the first-order integer-valued autoregressive process with Poisson innovations, based on binomial…
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…
In the era of big data, it is necessary to split extremely large data sets across multiple computing nodes and construct estimators using the distributed data. When designing distributed estimators, it is desirable to minimize the amount of…
The empirical probability density function for the conditional distribution of the true value of Poisson distribution parameter on one measurement is constructed by computer experiment. The analysis of the obtained distributions confirms…
Random fields are useful mathematical tools for representing natural phenomena with complex dependence structures in space and/or time. In particular, the Gaussian random field is commonly used due to its attractive properties and…
The Bell regression model (BRM) is a statistical model that is often used in the analysis of count data that exhibits overdispersion. In this study, we propose a Bayesian analysis of the BRM and offer a new perspective on its application.…
The repeated presentation of an identical visual stimulus in the receptive field of a neuron may evoke different spiking patterns at each trial. Probabilistic methods are essential to understand the functional role of this variance within…