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In this paper, we first transform a multivariate normal random vector into a random vector with elements that are approximately independent standard normal random variables. Then we propose the multivariate version generalized from the univariate normality test based on kurtosis from the literature. Power is investigated through the Monte Carlo Simulation with different significance level, dimension, and sample size. To assess the validity and accuracy of the new tests, we carry a comparative study with several other existing tests by selecting certain types of symmetric and asymmetric alternative distributions.

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In cricket, all-rounders play an important role. A good all-rounder should be able to contribute to the team by both bat and ball as needed. However, these players still have their dominant role by which we categorize them as batting all-rounders or bowling all-rounders. Current practice is to do so by mostly subjective methods. In this study, the authors have explored different machine learning techniques to classify all-rounders into bowling all-rounders or batting all-rounders based on their observed performance statistics. In particular, logistic regression, linear discriminant function, quadratic discriminant function, naïve Bayes, support vector machine, and random forest classification methods were explored. Evaluation of the performance of the classification methods was done using the metrics accuracy and area under the ROC curve. While all the six methods performed well, logistic regression, linear discriminant function, quadratic discriminant function, and support vector machine showed outstanding performance suggesting that these methods can be used to develop an automated classification rule to classify all-rounders in cricket. Given the rising popularity of cricket, and the increasing revenue generated by the sport, the use of such a prediction tool could be of tremendous benefit to decision-makers in cricket.

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