A probabilistic model for explaining the points achieved by a team in football competition. Forecasting and regression with applications to the Spanish competition

In the last decades, a lot of research papers applying statistical methods for analysing sports data have been published. Football, also called soccer, is one of the most popular sports all over the world organised in national championships in a round robin format in which the team reaching the most points at the end of the tournament wins the competition. The aim of this work is to develop a suitable probability model for studying the points achieved by a team in a football match. For this purpose, we built a discrete probability distribution taking values, zero for losing, one for a draw and three for a victory. We test its performance using data from the Spanish Football League (First division) during the 2013-14 season. Furthermore, the model provides an attractive framework for predicting points and incorporating covariates in order to study the factors affecting the points achieved by the teams.Peer Reviewe

Construction of multivariate distributions : a review of some recent results

The construction of multivariate distributions is an active field of research in theoretical and applied statistics. In this paper some recent developments in this field are reviewed. Specifically, we study and review the following set of methods: (a) Construction of multivariate distributions based on order statistics, (b) Methods based on mixtures, (c) Conditionally specified distributions, (d) Multivariate skew distributions, (e) Distributions based on the method of the variables in common and (f) Other methods, which include multivariate weighted distributions, vines and multivariate Zipf distributions

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

Testing for private information using trade duration models with unobserved market heterogeneity: The case of Banco Popular

In this paper, we attempt to assess the potential importance of different types of traders (i.e., those with public and private information) in financial markets using a specification of the standardized duration. This approach allows us to test unobserved heterogeneity in a nonlinear version based on a self-exciting threshold autoregressive conditional duration model. We illustrate the relevance of this procedure for identifying the presence of private information in the final days of trading of Banco Popular, the first bank rescued by the European Single Resolution Board

Aggregation of Dependent Risks in Mixtures of Exponential Distributions and Extensions

The distribution of the sum of dependent risks is a crucial aspect in actuarial sciences, risk management and in many branches of applied probability. In this paper, we obtain analytic expressions for the probability density function (pdf) and the cumulative distribution function (cdf) of aggregated risks, modeled according to a mixture of exponential distributions. We first review the properties of the multivariate mixture of exponential distributions, to then obtain the analytical formulation for the pdf and the cdf for the aggregated distribution. We study in detail some specific families with Pareto (Sarabia et al, 2016), Gamma, Weibull and inverse Gaussian mixture of exponentials (Whitmore and Lee, 1991) claims. We also discuss briefly the computation of risk measures, formulas for the ruin probability (Albrecher et al., 2011) and the collective risk model. An extension of the basic model based on mixtures of gamma distributions is proposed, which is one of the suggested directions for future research.The authors thanks to the Ministerio de Econom´ıa y Competitividad (projects ECO2016-76203-C2-1-P, JMS, FP and VJ ECO2013-47092 EGD) for partial support of this work. In addition, this work is part of the Research Project APIE 1/2015-17 (JMS, FP, VJ): “New methods for the empirical analysis of financial markets” of the Santander Financial Institute (SANFI) of UCEIF Foundation resolved by the University of Cantabria and funded with sponsorship from Banco Santander

Deriving Robust Bayesian Premiums under Bands of Prior Distributions with Applications

We study the propagation of uncertainty from a class of priors introduced by Arias-Nicolás et al. [(2016) Bayesian Analysis, 11(4), 1107–1136] to the premiums (both the collective and the Bayesian), for a wide family of premium principles (specifically, those that preserve the likelihood ratio order). The class under study reflects the prior uncertainty using distortion functions and fulfills some desirable requirements: elicitation is easy, the prior uncertainty can be measured by different metrics, and the range of quantities of interest is easily obtained from the extremal members of the class. We illustrate the methodology with several examples based on different claim counts models

A bivariate response model for studying the marks obtained in two jointly-dependent modules in higher education

We study the factors which may affect students' marks in two modules, mathematics and statistics, taught consecutively in the first year of a Business Administration Studies degree course. For this purpose, we introduce a suitable bivariate regression model in which the dependent variables have bounded support and the marginal means are functions of explanatory variables. The marginal probability density functions have a classical beta distribution. Simulation experiments were performed to observe the behaviour of the maximum likelihood estimators. Comparisons with univariate beta regression models show the proposed bivariate regression model to be superior