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Modeling wind speed data is the prime requirement for harnessing the wind energy potential at a given site. While the Weibull distribution is the most commonly employed distribution in the literature and in practice, numerous scientific articles have proposed various alternative continuous probability distributions to model the wind speed at their convenient sites. Fitting the best distribution model to the data enables the practitioners to estimate the wind power density more accurately, which is required for wind power generation. In this paper we comprehensively review fourteen continuous probability distributions, and investigate their fitting capacities at seventeen locations of India covering the east and west offshore corner as well as the mainland, which represents a large variety of climatological scenarios. A first main finding is that wind speed varies a lot inside India and that one should treat each site individually for optimizing wind power generation. A second finding is that the wide acceptance of the Weibull distribution should at least be questioned, as it struggles to represent wind regimes with heterogeneous data sets exhibiting multimodality, high levels of skewness and/or kurtosis. Our study reveals that mixture distributions are very good alternative candidates that can model difficult shapes and yet do not require too many parameters. [ABSTRACT FROM AUTHOR]

Compositional data have peculiar characteristics that pose significant challenges to traditional statistical methods and models. Within this framework, we use a convenient mode parametrized Dirichlet distribution across multiple fields of statistics. In particular, we propose finite mixtures of unimodal Dirichlet (UD) distributions for model-based clustering and classification. Then, we introduce the contaminated UD (CUD) distribution, a heavy-tailed generalization of the UD distribution that allows for a more flexible tail behavior in the presence of atypical observations. Thirdly, we propose finite mixtures of CUD distributions to jointly account for the presence of clusters and atypical points in the data. Parameter estimation is carried out by directly maximizing the maximum likelihood or by using an expectation-maximization (EM) algorithm. Two analyses are conducted on simulated data to illustrate the effects of atypical observations on parameter estimation and data classification, and how our proposals address both aspects. Furthermore, two real datasets are investigated and the results obtained via our models are discussed. [ABSTRACT FROM AUTHOR]

Insurance loss data have peculiar features that can rarely be accounted for by simple parametric distributions. Thus, in this manuscript, we first introduce a new type of location mixture model: the mode mixture. By using convenient mode-parameterized hump-shaped distributions, we present a family of eight mode mixture of unimodal distributions. Then, we fit these models to two real insurance loss datasets, where they are evaluated in terms of goodness of fit and ability to reproduce classical risk measures. We extend the comparisons to existing models based on mode-parameterized hump-shaped distributions. Lastly, using simulated data, we further investigate the performance of the estimated risk measures of our models. [ABSTRACT FROM AUTHOR]