A mixture of multivariate contaminated normal distributions is developed for model-based clustering. In addition to the parameters classical mixture, our has, each cluster, a parameter controlling proportion mild outliers and one specifying degree contamination. Crucially, these do not have be specified priori, adding flexibility approach. Parsimony introduced via eigen-decomposition component covariance matrices, sufficient conditions identifiability all members resulting family are...

Insurance and economic data are often positive, we need to take into account this peculiarity in choosing a statistical model for their distribution. An example is the inverse Gaussian (IG), which one of most famous considered distributions with positive support. With aim increasing use IG distribution on insurance data, propose convenient mode-based parameterization yielding reparametrized (rIG) distribution; it allows/simplifies various branches statistics, give some examples. In...

Abstract This article proposes the elliptical multivariate leptokurtic‐normal (MLN) distribution to fit data with excess kurtosis. The MLN is a Gram–Charlier expansion of normal (MN) and has closed‐form representation characterized by one additional parameter denoting It obtained from MN distribution, reshaping its generating variate associated orthogonal polynomials. strength this approach for obtaining lies in general applicability as it can be applied any law get suitable data. Maximum...

Insurance and economic data are frequently characterized by positivity, skewness, leptokurtosis, multi-modality; although many parametric models have been used in the literature, often these peculiarities call for more flexible approaches. Here, we propose a finite mixture of contaminated gamma distributions that provides better characterization data. It is placed between non-parametric density estimation strikes balance alternatives, as large class densities can be implemented. We adopt...

Cluster-weighted models (CWMs) are mixtures of regression with random covariates. However, besides having recently become rather popular in statistics and data mining, there is still a lack support for CWMs within the most statistical suites. In this paper, we introduce flexCWM, an R package specifically conceived fitting CWMs. The supports modeling conditioned response variable by means common distributions exponential family t distribution. Covariates allowed to be mixed-type parsimonious...

Summary This study explores the crucial task of determining optimal number components in mixture models, known as order, when considering matrix‐variate data. Despite growing interest this data type among practitioners and researchers, effectiveness information criteria selecting order remains largely unexplored branch literature. Although Bayesian criterion (BIC) is commonly utilised, its only marginally tested context, several other potentially valuable exist. An extensive simulation...

In medical and health research, investigators are often interested in countable quantities such as hospital length of stay (e.g., days) or the number doctor visits. Poisson regression is commonly used to model count data, but this approach can’t accommodate overdispersion—when variance exceeds mean. To address issue, negative binomial (NB) distribution (NB-D) and, by extension, NB provide a well-documented alternative. However, real-data applications present additional challenges that must...

In the context of mixture models with random covariates, this article presents polynomial Gaussian cluster-weighted model (CWM). It extends linear CWM, for bivariate data, in a twofold way. First, it allows possible nonlinear dependencies components by considering regression. Second, is not restricted to be used model-based clustering only being contextualized most general classification framework. Maximum likelihood parameter estimates are derived using EM algorithm and selection carried...

The Gaussian hidden Markov model (HMM) is widely considered for the analysis of heterogenous continuous multivariate longitudinal data. To robustify this approach with respect to possible elliptical heavy-tailed departures from normality, due presence outliers, spurious points, or noise (collectively referred as bad points herein), contaminated HMM here introduced. distribution represents an generalization and allows automatic detection in same natural way observations are typically assigned...

Item response theory (IRT) models are a class of statistical used to describe the behaviors individuals set items having certain number options. They adopted by researchers in social science, particularly analysis performance or attitudinal data, psychology, education, medicine, marketing and other fields where aim is measure latent constructs. Most IRT analyses use parametric that rely on assumptions often not satisfied. In such cases, nonparametric approach might be preferable;...

We introduce the R package ContaminatedMixt, conceived to disseminate use of mixtures multivariate contaminated normal distributions as a tool for robust clustering and classification under common assumption elliptically contoured groups. Thirteen variants model are also implemented parsimony. The expectationconditional maximization algorithm is adopted obtain maximum likelihood parameter estimates, likelihood-based selection criteria used select number Parallel computation can be on...

A correct modelization of the insurance losses distribution is crucial in industry. This generally highly positively skewed, unimodal hump-shaped, and with a heavy right tail. Compound models are profitable way to accommodate situations which some probability masses shifted tails distribution. Therefore, this work, general approach compound hump-shaped distributions mixing dichotomous introduced. 2-parameter distribution, defined on positive support, considered reparametrized respect mode...