Statistics for Spatial Data.

The art of parameter(s) induction to the baseline distribution has received a great deal of attention in recent years. The induction of one or more additional shape parameter(s) to the baseline distribution makes the distribution more flexible especially for studying the tail properties. This parameter(s) induction also proved helpful in improving the goodness-of-fit of the proposed generalized family of distributions. There exist many generalized (or generated) G families of continuous univariate distributions since 1985. In this paper, the well-established and widely-accepted G families of distributions like the exponentiated family, Marshall-Olkin extended family, beta-generated family, McDonald-generalized family, Kumaraswamy-generalized family and exponentiated generalized family are discussed. We provide lists of contributed literature on these well-established G families of distributions. Some extended forms of the Marshall-Olkin extended family and Kumaraswamy-generalized family of distributions are proposed.

/pdf/parameter-induction-in-continuous-univariate-distributions-2fox66b9xz.pdf

Parameter induction in continuous univariate distributions: Well-established G families

Advanced Multivariate Statistics With Matrices

Mainstream statistical methodology is generally applicable to data observed in Euclidean space. There are, however, numerous contexts of considerable scientific interest in which the natural supports for the data under consideration are Riemannian manifolds like the unit circle, torus, sphere, and their extensions. Typically, such data can be represented using one or more directions, and directional statistics is the branch of statistics that deals with their analysis. In this paper, we provide a review of the many recent developments in the field since the publication of Mardia and Jupp (Wiley 1999), still the most comprehensive text on directional statistics. Many of those developments have been stimulated by interesting applications in fields as diverse as astronomy, medicine, genetics, neurology, space situational awareness, acoustics, image analysis, text mining, environmetrics, and machine learning. We begin by considering developments for the exploratory analysis of directional data before progressing to distributional models, general approaches to inference, hypothesis testing, regression, nonparametric curve estimation, methods for dimension reduction, classification and clustering, and the modelling of time series, spatial and spatio-temporal data. An overview of currently available software for analysing directional data is also provided, and potential future developments are discussed.

Recent advances in directional statistics

This paper addresses different methods of estimation of the unknown parameters of a two-parameter Kumaraswamy distribution from a frequentist point of view. We briefly describe ten different frequentist approaches, namely, maximum likelihood estimators, moments estimators, L-moments estimators, percentile based estimators, least squares estimators, weighted least squares estimators, maximum product of spacings estimators, Cramer–von-Mises estimators, Anderson–Darling estimators and right tailed Anderson–Darling estimators. Monte Carlo simulations and two real data applications are performed to compare the performances of the estimators for both small and large samples.

Kumaraswamy distribution: different methods of estimation

We consider a new generalization of the skew-normal distribution introduced by Azzalini (1985). We denote this distribution Beta skew-normal (BSN) since it is a special case of the Beta generated distribution (Jones, 2004). Some properties of the BSN are studied. We pay attention to some generalizations of the skew-normal distribution (Bahrami et al., 2009; Sharafi and Behboodian, 2008; Yadegari et al., 2008) and to their relations with the BSN.

https://people.unica.it/musio/files/2008/10/CS2013.pdf

A Generalization of the Skew-Normal Distribution: The Beta Skew-Normal

Nanosheets of two mixed linker (anilate/carboxylate)/YbIII-based two-dimensional (2D) layered coordination polymers (CPs) are herein reported. Bulky sized CPs, formulated as [Yb4(ClCNAn)5(DOBDC)1(D...

Heteroleptic NIR-Emitting YbIII/Anilate-Based Neutral Coordination Polymer Nanosheets for Solvent Sensing

Standard Bayesian analyses can be difficult to perform when the full likelihood, and consequently the full posterior distribution, is too complex or even impossible to specify or if robustness with respect to data or to model misspecifications is required. In these situations, we suggest to resort to a posterior distribution for the parameter of interest based on proper scoring rules. Scoring rules are loss functions designed to measure the quality of a probability distribution for a random variable, given its observed value. Important examples are the Tsallis score and the Hyvarinen score, which allow us to deal with model misspecifications or with complex models. Also the full and the composite likelihoods are both special instances of scoring rules. The aim of this paper is twofold. Firstly, we discuss the use of scoring rules in the Bayes formula in order to compute a posterior distribution, named SR-posterior distribution, and we derive its asymptotic normality. Secondly, we propose a procedure for building default priors for the unknown parameter of interest that can be used to update the information provided by the scoring rule in the SR-posterior distribution. In particular, a reference prior is obtained by maximizing the average $$\alpha $$
 -divergence from the SR-posterior distribution. For $$0 \le |\alpha |<1$$
 , the result is a Jeffreys-type prior that is proportional to the square root of the determinant of the Godambe information matrix associated with the scoring rule. Some examples are discussed.

Objective Bayesian inference with proper scoring rules

The Kumaraswamy skew-normal distribution

In this work, industrial waste hexafluorosilicic acid (H2SiF6 or FSA) has been proven to be a low-cost alternative to silicate esters for the synthesis of high-quality MCM-41 (high surface area, hi...

Valentina Mameli

Papers

A Generalization of the Skew-Normal Distribution: The Beta Skew-Normal

Heteroleptic NIR-Emitting YbIII/Anilate-Based Neutral Coordination Polymer Nanosheets for Solvent Sensing

Objective Bayesian inference with proper scoring rules

The Kumaraswamy skew-normal distribution

Hexafluorosilicic Acid (FSA): from Hazardous Waste to Precious Resource in Obtaining High Value-Added Mesostructured Silica