We can use both normal and the Laplace distribution to analyze the symmetrical data. The only differences the Normal distribution is used to analyze the symmetrical data when it has a short tail whereas the Laplace distribution is used when the data has long tail. In the case of moderate sample size, we can use any of the above two distribution namely Normal or Laplace distribution. Therefore it is important to choose the best possible decision for the distribution assumptions (N Balakrishnan, 2007)

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