The paper presents a forecasting model for association football scores. The model uses a Weibullinter-arrival times based count process and a copula to produce a bivariate distribution for the number of goals scored by the home and away teams in a match. We test it against a variety of alternatives, including the simpler Poisson distribution-based model and an independent version of our model. The out-of-sample performance of our methodology is illustrated first using calibration curves and then in a Kelly-type betting strategy that is applied to the pre-match win/draw/loss market and to the over-under 2.5 goals market. The new model provides an improved fit to data compared to previous models and results in positive returns to betting.

In this paper we consider the estimation of the parameters of the spatio-temporal covariances of spatio-temporal stationary random processes. We define Finite Fourier Transforms of the processes at each location and based on joint distribution of these complex valued random variables we define an approximate likelihood function and consider the maximization. Ideas are similar to Whittle likelihood function considered in time series. The sampling properties of the estimators are investigated. The method is applied to simulated data and also to pacific wind speed data considered earlier by Cressie and Huang [6].

We propose several measures, functional and scalar, for asymmetry of distributions by comparing the behavior of probability densities to the right and left of the mode(s) and show how to generate classes of equivalent distributions from a given distribution, allowing for varying asymmetry but retaining some information theoretic properties of the original distribution, such as the entropy. r

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