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This article draws attention to a comparative study of different members within the inverse Weibull Power Series (IWPS) to analyze the COVID-19 data from South Africa for the period from 27 March to 23 August 2020. A new sibling of the IWPS is introduced, namely the inverse Weibull negative binomial. An EM algorithm is developed for computing the maximum likelihood estimates of the model parameters. The IWPS growth curve model and its special cases are used for prediction of the COVID-19 spread in South Africa. It is found that the IWPS model fits the disease growth of the COVID-19 confirmed cases well with worthy long-term predictions. The IWPS growth curve modeling of South African predicts that the number of confirmed new cases will decrease at the end of November 2020. [ABSTRACT FROM AUTHOR]

This paper introduces a new family of matrix variate distributions based on the mean-mixture of normal (MMN) models. The properties of the new matrix variate family, namely stochastic representation, moments and characteristic function, linear and quadratic forms as well as marginal and conditional distributions are investigated. Three special cases including the restricted skew-normal, exponentiated MMN and the mixed-Weibull MMN matrix variate distributions are presented and studied. Based on the specific presentation of the proposed model, an EM-type algorithm can be directly implemented for obtaining maximum likelihood estimate of the parameters. The usefulness and practical utility of the proposed methodology are illustrated through two conducted simulation studies and through the Landsat satellite dataset analysis. [ABSTRACT FROM AUTHOR]

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]