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- Distribution view: a tool to write and simulate distributionsPublication . Coelho, José; Branco, Fernando; Oliveira, TeresaIn our work we present a tool to write and simulate distributions. This tool allows to write mathematical expressions which can contain not only functions and variables, but also statistical distributions, including mixtures. Each time the expression is evaluated, for all inner distributions, is generated a value according to the distribution and is used for expression value determination. The inversion method can be used in this language, allowing to generate all distributions that have an expression for cdf inverse. The variables in the language allow the generation of several correlated distributions. To illustrate the advantages of using distribution view we present two applications: One in Project Risk Management, compares the PERT method with Simulation alternative; The other in Statistics, compares the Power of Randomization Test with the power of Student-t Test , using the set of Marron-Wand distributions.
- The impact of distributional shape on the power of randomization tests for two independent groups: a simulation study using small balanced samplesPublication . Branco, Fernando; Oliveira, Teresa; Oliveira, AmilcarThe importance of randomization tests is very well known in experimental research, particularly in biometry. The aim of the resent research is to evaluate the impact of distributional shape on the power of the randomization test for difference between the means of two independent groups (with n1=n2=16). To manipulate shape in terms of asymmetry and kurtosis, we used g-and-h distributions. We evaluated the power of the randomization test, and also the power of the Student-t test, as a comparison standard, with data simulated from 12 g-and-h distributions for seven values of effect size. For each condition, we generated 20000 samples, and for each one the power of randomization tests was estimated using 1000 permutations. We set the value of Type I error probability at 0.05. The results show gains in power for both tests with increasing skewness and/or kurtosis, with a slight advantage for the randomization tests over the Student-t test.