• Journal of the Korean Statistical Society
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• v.27 no.3
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• pp.289-303
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• 1998

For square contingency tables with ordered categories, Tomizawa (1995) considered two kinds of measures to represent the degree of departure from global symmetry, which means that the probability that an observation will fall in one of cells in the upper-right triangle of square table is equal to the probability that the observation falls in one of cells in the lower-left triangle of it. This paper proposes a generalization of those measures. The proposed measure is expressed by using Cressie and Read's (1984) power divergence or Patil and Taillie's (1982) diversity index. Special cases of the proposed measure include TomiBawa's measures. The proposed measure would be useful for comparing the degree of departure from global symmetry in several tables.

• The Korean Journal of Applied Statistics
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• v.27 no.2
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• pp.249-261
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• 2014

Ever increasing "Big data" can only be effectively processed by parallel computing. Parallel computing refers to a high performance computational method that achieves effectiveness by dividing a big query into smaller subtasks and aggregating results from subtasks to provide an output. However, it is well-known that parallel computing does not achieve scalability which means that performance is improved linearly by adding more computers because it requires a very careful assignment of tasks to each node and collecting results in a timely manner. Hadoop is one of the most successful platforms to attain scalability. In this paper, we propose a measurement for Hadoop optimization by utilizing a Lorenz curve which is a proxy for the inequality of hardware resources. Our proposed index takes into account the intrinsic overhead of Hadoop systems such as CPU, disk I/O and network. Therefore, it also indicates that a given Hadoop can be improved explicitly and in what capacity. Our proposed method is illustrated with experimental data and substantiated by Monte Carlo simulations.