Related papers: Tests for zero-inflation and overdispersion
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…
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…
The scan statistic is widely used in spatial cluster detection applications of inhomogeneous Poisson processes. However, real data may present substantial departure from the underlying Poisson process. One of the possible departures has to…
Generalized linear models (GLMs) using a regression procedure to fit relationships between predictor and target variables are widely used in automobile insurance data. Here, in the process of ratemaking and in order to compute the premiums…
This research deals with the estimation and imputation of missing data in longitudinal models with a Poisson response variable inflated with zeros. A methodology is proposed that is based on the use of maximum likelihood, assuming that data…
The Tweedie generalized linear models are commonly applied in the insurance industry to analyze semicontinuous claim data. For better prediction of the aggregated claim size, the mean and dispersion of the Tweedie model are often estimated…
We propose a new framework for the modelling of count data exhibiting zero inflation (ZI). The main part of this framework includes a new and more general parameterisation for ZI models which naturally includes both over- and…
In microbiome studies, it is of interest to use a sample from a population of microbes, such as the gut microbiota community, to estimate the population proportion of these taxa. However, due to biases introduced in sampling and…
Dimension reduction of high-dimensional microbiome data facilitates subsequent analysis such as regression and clustering. Most existing reduction methods cannot fully accommodate the special features of the data such as count-valued and…
The Poisson distribution is the default choice of likelihood for probabilistic models of count data. However, due to the equidispersion contraint of the Poisson, such models may have predictive uncertainty that is artificially inflated.…
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…
Imputation of missing values is a strategy for handling non-responses in surveys or data loss in measurement processes, which may be more effective than ignoring them. When the variable represents a count, the literature dealing with this…
Count data with zero inflation and large outliers are ubiquitous in many scientific applications. However, posterior analysis under a standard statistical model, such as Poisson or negative binomial distribution, is sensitive to such…
The zero-inflated logistic regression model accommodates binary responses with excess zeros, which often arise from a latent mixture of susceptible and insusceptible subpopulations or asymmetric misclassification of the response. The model…
This paper describes a compound Poisson-based random effects structure for modeling zero-inflated data. Data with large proportion of zeros are found in many fields of applied statistics, for example in ecology when trying to model and…
We consider the complex data modeling problem motivated by the zero-inflated and overdispersed data from microbiome studies. Analyzing how microbiome abundance is associated with human biological features, such as BMI, is of great…
Zero-inflated models are frequently used to deal with data having many zeros. A commonly used model for over-dispersed data containing zeros is known as the zero-inflated Poisson model. However, to account for the heterogeneity of counts…
Weighted networks encode not only the presence of interactions but also their strength. Existing methods for weighted network community detection often rely on Poisson models, which can be restrictive for overdispersed data and make…
This paper proposes a method for analyzing count time series with inflation or deflation of zeros. In particular, zero-modified Poisson and zero-modified negative binomial series with intensities generated by non-negative Markov sequences…
We propose a new powerful family of tests of univariate normality. These tests are based on an initial value problem in the space of characteristic functions originating from the fixed point property of the normal distribution in the zero…