Statistical Inference for a General Family of Modified Exponentiated Distributions

In this paper, a modified exponentiated family of distributions is introduced. The new model was built from a continuous parent cumulative distribution function and depends on a shape parameter. Its most relevant characteristics have been obtained: the probability density function, quantile function, moments, stochastic ordering, Poisson mixture with our proposal as the mixing distribution, order statistics, tail behavior and estimates of parameters. We highlight the particular model based on the classical exponential distribution, which is an alternative to the exponentiated exponential, gamma and Weibull. A simulation study and a real application are presented. It is shown that the proposed family of distributions is of interest to applied areas, such as economics, reliability and finances.

Spatial identification of component-based relative risks

This article aims at identifying the high risk provinces in Iraq using a finite Poisson mixture. Through this methodology, the levels of relative risk is determined through identifying the number of components. In this article we do not investigate spatial correlation among regions and assume that the levels of risk observed in different regions are independent each other. The estimation of the model parameters and the model selection are performed using the Bayesian approach which allow to allocate each province to an identified risk level. We consider the data of the Coronavirus disease (COVID-19) infections in 18 provinces in Iraq and determining the levels of relative risks of this pandemic. The results are spatially shown in map which illustrates that the best Bayesian model fitted the data is 3 components model (high, medium and low risk).

Quantifying superspreading for COVID-19 using Poisson mixture distributions

The number of secondary cases is an important parameter for the control of infectious diseases. When individual variation in disease transmission is present, like for COVID-19, the number of secondary cases is often modelled using a negative binomial distribution. However, this may not be the best distribution to describe the underlying transmission process. We propose the use of three other offspring distributions to quantify heterogeneity in transmission, and we assess the possible bias in estimates of the offspring mean and its overdispersion when the data generating distribution is different from the one used for inference. We find that overdispersion estimates may be biased when there is a substantial amount of heterogeneity, and that the use of other distributions besides the negative binomial should be considered. We revisit three previously analysed COVID-19 datasets and quantify the proportion of cases responsible for 80% of transmission, p80%, while acknowledging the variation arising from the assumed offspring distribution. We find that the number of secondary cases for these datasets is better described by a Poisson-lognormal distribution.

EL SAPO ARLEQUÍN DEL CHOCÓ (Atelopus spurrelli Boulenger, 1914) EN EL PARQUE NACIONAL NATURAL UTRÍA, COLOMBIA: DENSIDAD POBLACIONAL Y RECOMENDACIONES PARA SU MONITOREO Y CONSERVACIÓN

Se evaluó la densidad poblacional de Atelopus spurrelli en el Parque Nacional Natural Utría para generar la línea base que permita establecer un programa de seguimiento y monitoreo de la especie, así como evaluar el efecto de potenciales amenazas sobre esta población. Se seleccionaron tres quebradas con registros previos de la especie en el Parque Natural y se inspeccionaron 7 transectos de longitud variable. La densidad poblacional se estimó con el método de muestreo por distancias usando el modelo Multinomial-Poisson Mixture. Se registraron un total de 191 individuos de A. spurrelli con una densidad de 0,09 individuos/m2 (IC 95%: 0,07-0,12) en la quebrada Cocalito, 0,13 (0,1-0,18) en la quebrada La Aguada y 0,14 (0,10-0,19) en Guachalito. La quebrada Cocalito presentó la más baja densidad promedio estimada, lo que sugiere un factor biofísico o antrópico diferencial entre quebradas que tenga un efecto sobre este parámetro poblacional. Se sugiere realizar el seguimiento de la población en varios periodos del año y multianual, para determinar si las diferencias en la densidad de la especie entre quebradas y en comparación a estudios previos son artefactos de los métodos de análisis, representatividad del muestreo o respuestas a factores biofísicos y antrópicos presentes de manera diferencial en las quebradas muestreadas.

Identifying heterogeneity in the risk factors of dental caries status in Chinese adolescents using Poisson mixture regression

ObjectiveThe purpose of this study was to cluster individuals into groups with different dental health characteristics and make statistical inferences on the effect differences among different groups simultaneously to identify the heterogeneity of risk factors in Chinese adolescents by analysing the data from the 4th Chinese National Oral Health Survey.MethodsFor decayed, missing and filled permanent teeth (DMFT), mean values were statistically analysed for their relationships with different categories of all involved variables. As DMFT scores only have discrete values, Poisson mixture regression was adopted to model the heterogeneity and complex patterns in the association and to detect the subgroup. The Bayesian information criterion (BIC) was used to determine the optimal number of subgroups. A series of Wald tests were used to explore the relationship between risk factors including the interaction effects and the number of DMFT.ResultsA total of 100 986 individuals aged 12–15 years old were analysed. The model clustered different individuals into three subgroups and built three submodels for detailed statistical inference simultaneously. The number of individuals in the three subgroups were 52 576 (52.1%), 41 969 (41.5%) and 6441 (6.4%), respectively. The mean (SD) of DMFT of the three subgroups was 0.50 (1.05), 0.99 (1.21), 5.59 (2.50). The model fitting results indicated that the effects of all risk factors on DMFT appear to be different in three subgroups. Controlling the confounding effects, our analysis implied that the regional inequality was the main contributing factor to dental caries among adolescents in Chinese mainland.ConclusionsThe risk factors of dental caries exhibited heterogeneity in groups with different characteristics. The Poisson mixture regression model could cluster individuals into groups and identify the heterogeneous effects of risk factors among different groups. The findings support the need for different targeted interventions and prevention measures in groups with different dental health characteristics.

Multivariate Collective Risk Model: Dependent Claim Numbers and Panjer’s Recursion

In this paper, we discuss a generalization of the collective risk model and of Panjer’s recursion. The model we consider consists of several business lines with dependent claim numbers. The distributions of the claim numbers are assumed to be Poisson mixture distributions. We let the claim causes have certain dependence structures and prove that Panjer’s recursion is also applicable by finding an appropriate equivalent representation of the claim numbers. These dependence structures are of a stochastic non-negative linear nature and may also produce negative correlations between the claim causes. The consideration of risk groups also includes dependence between claim sizes. Compounding the claim causes by common distributions also keeps Panjer’s recursion applicable.

A Gamma-Poisson Mixture Topic Model for Short Text

Most topic models are constructed under the assumption that documents follow a multinomial distribution. The Poisson distribution is an alternative distribution to describe the probability of count data. For topic modelling, the Poisson distribution describes the number of occurrences of a word in documents of fixed length. The Poisson distribution has been successfully applied in text classification, but its application to topic modelling is not well documented, specifically in the context of a generative probabilistic model. Furthermore, the few Poisson topic models in the literature are admixture models, making the assumption that a document is generated from a mixture of topics. In this study, we focus on short text. Many studies have shown that the simpler assumption of a mixture model fits short text better. With mixture models, as opposed to admixture models, the generative assumption is that a document is generated from a single topic. One topic model, which makes this one-topic-per-document assumption, is the Dirichlet-multinomial mixture model. The main contributions of this work are a new Gamma-Poisson mixture model, as well as a collapsed Gibbs sampler for the model. The benefit of the collapsed Gibbs sampler derivation is that the model is able to automatically select the number of topics contained in the corpus. The results show that the Gamma-Poisson mixture model performs better than the Dirichlet-multinomial mixture model at selecting the number of topics in labelled corpora. Furthermore, the Gamma-Poisson mixture produces better topic coherence scores than the Dirichlet-multinomial mixture model, thus making it a viable option for the challenging task of topic modelling of short text.