Evaluating wind speed probability distribution models with a novel goodness of fit metric: a Trinidad and Tobago case study

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Abstract Wind energy has been explored as a viable alternative to fossil fuels in many small island developing states such as those in the Caribbean for a long time. Central to evaluating the feasibility of any wind energy project is choosing the most appropriate wind speed model. This is a function of the metric used to assess the goodness of fit of the statistical models tested. This paper compares a number of common metrics then proposes an alternative to the application-blind statistical tools commonly used.Wind speeds at two locations are considered: Crown Point, Tobago; and Piarco, Trinidad. Hourly wind speeds over a 15-year period have been analyzed for both sites. The available data is modelled using the Birnbaum–Saunders, Exponential, Gamma, Generalized Extreme Value, Generalized Pareto, Nakagami, Normal, Rayleigh and Weibull probability distributions. The distributions were compared graphically and their parameters were estimated using maximum likelihood estimation. Goodness of fit was assessed using the normalised mean square error testing, Chi-squared testing, Kolmogorov–Smirnov, R-squared, Akaike information criteria and Bayesian information criteria tests and the distributions ranked. The distribution ranking varied widely depending on the test used highlighting the need for a more contextualized goodness of fit metric. With this in mind, the concept of application-specific information criteria (ASIC) for testing goodness of fit is introduced. This allows distributions to be ranked by secondary features which are a function of both the primary data and the application space.
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