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...

The research objective of this paper is to handle situations where the empirical distribution multivariate real-valued data elliptical and with heavy tails. Many statistical models already exist that accommodate these peculiarities. This enriches branch literature by introducing tail-inflated normal (MTIN) distribution, an tails generalization (MN). MTIN belongs family MN scale mixtures choosing a convenient continuous uniform as mixing distribution. Moreover, it has closed-form for...

We introduce multivariate models for the analysis of stock market returns. Our are developed under hidden Markov and semi-Markov settings to describe temporal evolution returns, whereas marginal distribution returns is described by a mixture leptokurtic-normal (LN) distributions. Compared normal distribution, LN has an additional parameter governing excess kurtosis this allows us better fit both distributional dynamic properties daily outline expectation maximization algorithm maximum...

In some areas of Estonia, groundwater contains a significant number natural radionuclides, especially radium isotopes, which may cause radiation protection concern depending on the geological structure aquifer. Indeed, parametric value 0.1 mSv y⁻¹ for total indicative dose established by European Directive 98/83/EC, adopted as limit in Estonian national legislation, is often exceeded. A Twinning Project between Estonia and Italy was carried out within framework Transition Facility Programme,...

Abstract In allometric studies, the joint distribution of log‐transformed morphometric variables is typically elliptical and with heavy tails. To account for these peculiarities, we introduce multivariate shifted exponential normal (MSEN) , an heavy‐tailed generalization (MN). The MSEN belongs to family MN scale mixtures (MNSMs) by choosing a convenient as mixing distribution. probability density function has simple closed‐form characterized only one additional parameter, respect nested MN,...

In this article the serial dependences between observed time series and lagged series, taken into account one‐by‐one, are graphically analysed by what we have chosen to call ‘autodependogram’. This tool is a sort of natural nonlinear counterpart well‐known autocorrelogram used in linear context. The autodependogram based on simple idea using, instead autocorrelations at varying lags, χ 2 ‐test statistics applied convenient contingency tables. efficacy graphical device confirmed real...

Abstract This article enlarges the covariance configurations, on which classical linear discriminant analysis is based, by considering four models arising from spectral decomposition when eigenvalues and/or eigenvectors matrices are allowed to vary or not between groups. As in approach, assessment of these configurations accomplished via a test training set. The discrimination rule then built upon configuration provided test, unlabeled data. Numerical experiments, simulated and real data,...

Abstract Many statistical problems involve the estimation of a $$\left( d\times d\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mfenced><mml:mi>d</mml:mi><mml:mo>×</mml:mo><mml:mi>d</mml:mi></mml:mfenced></mml:math> orthogonal matrix $$\varvec{Q}$$ xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Q</mml:mi></mml:mrow></mml:math> . Such an is often challenging due to orthonormality constraints on To cope with this problem, we use well-known PLU...

The proposed multiple scaled contaminated asymmetric Laplace (MSCAL) distribution is an extension of the multivariate to allow for a different excess kurtosis on each dimension and more flexible shapes hyper-contours. These peculiarities are obtained by working principal component (PC) space. structure MSCAL has further advantage allowing automatic PC-wise outlier detection – i.e., outliers separately PC when convenient constraints parameters imposed. fitted using Monte Carlo...

Abstract Recent studies about cryptocurrency returns show that their distribution can be highly-peaked, skewed, and heavy-tailed, with a large excess kurtosis. To accommodate all these peculiarities, we propose the asymmetric Laplace scale mixture (ALSM) family of distributions. Each member is obtained by dividing parameter conditional (AL) convenient mixing random variable taking values on or part positive real line whose depends vector $$\varvec{\theta }$$ <mml:math...

Detecting and measuring lag-dependencies is very important in time-series analysis. This study commonly carried out by focusing on the linear via well-known autocorrelogram. However, practice, there are many situations which autocorrelogram fails because of nonlinear structure serial dependence. To cope with this problem, paper R package SDD introduced. Among available approaches to analyze an omnibus way, considers autodependogram some its variants. The autodependogram, defined computing...

Abstract Quite often real data exhibit non-normal features, such as asymmetry and heavy tails, present a latent group structure. In this paper, we first propose the multivariate skew shifted exponential normal distribution that can account for these characteristics. Then, use in finite mixture modeling framework. An EM algorithm is illustrated maximum-likelihood parameter estimation. We provide simulation study compares fitting performance of our model with those several alternative models....

Abstract Real data is taking on more and complex structures, raising the necessity for flexible parsimonious statistical methodologies. Tensor-variate (or multi-way) structures are a typical example of such kind data. Unfortunately, real often present atypical observations that make traditional normality assumption inadequate. Thus, in this paper, we first introduce two new tensor-variate distributions, both heavy-tailed generalizations normal distribution. Then, use these distributions...