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In this paper, we characterize symmetric distributions based on Renyi entropy of order statistics in subsamples. A test of symmetry is proposed based on the estimated Renyi entropy. Critical values of the test are computed by Monte Carlo simulation. Also we compute the power of the test under different alternatives and show that it behaves better that the test of Habibi and Arghami (1386).

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In this paper a new version of skew uniform distribution is introduced which is completely different from the previous works. Some important properties of the new distribution contain the expression for the density and distribution, kth moments, moment generating and characteristic functions, variance, skewness and kurtusis, mean deviation from the mean, median and mode and parameter estimation are investigated. Also a simulation study on this distribution is carried out to show the consistency of the maximum likelihood and moments estimators. In the end, the new skew uniform distribution is compared with uniform distribution.

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Maximum of the Renyi entropy and the Tsallis entropy are generalization of the maximum entropy for a larger class of Shannon entropy. In this paper we introduce the maximum Renyi entropy and some of the attributes of distributions which have maximum Renyi entropy investigated. The form of distributions with maximum Renyi entropy is power so we state some properties of these distributions and we have a new form of the Renyi entropy. After pointing the topics of minimum Renyi divergence, some other points in this relation have been discussed. An another form of Renyi divergence have also obtained. Therefore we discussed some of the economic applications of the maximum entropy. Meanwhile, the review of the Csiszar information measure, the general form of distributions with minimum Renyi divergence have obtained.