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

Discrete generalized half-normal distribution and its applications in quantile regression

A new discrete two-parameter distribution is introduced by discretizing a generalized half-normal distribution. The model is useful for fitting overdispersed as well as underdispersed data. The failure function can be decreasing, bathtub shaped or increasing. A reparameterization of the distribution is introduced for use in a regression model based on the median. The behaviour of the maximum likelihood estimates is studied numerically, showing good performance in finite samples. Three real data set applications reveal that the new model can provide a better explanation than some other competitors

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

La distribución binominal-exponencial truncada con aplicaciones en el sector del seguro de automóviles

ABSTRACT. In this paper we present a new claim count distribution with overdispersion. The new distribution is obtained by mixing the p parameter in the binomial distribution with a (0,1) truncated exponential distribution. The new distribution can be considered as an alternative to the classical Poisson, binomial and geometric distributions. Some properties of the new distribution and some applications in the field of automobile insurance are given, by fitting empirical claim data and obtaining bonus-malus premiums.RESUMEN. En este trabajo se presenta una nueva distribución de conteo que puede presentar sobredispersión. La distribución se obtiene como mezcla del parámetrro p de la distribución binomial con la distribución exponencial truncada en el intervalo (0,1). La nueva distribución puede considerarse una alternativa a las distribuciones clásicas de Poisson, binomial y geométrica. Se muestran algunas propiedades de esta nueva distribución, así como aplicaciones en el ramo de seguro de automóviles mediante el ajuste de datos empíricos de reclamaciones y cálculo de primas bonus-malus

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