ABSTRACT The variance of the log-likelihood function, which is called varentropy, is a measure of the concentration of information content around the Shannon entropy. This measure is widely applied in finite blocklength information theory and data compression. On the other hand, in the field of statistics, this measure has been used as an alternative of the kurtosis measure for continuous density functions that has a better performance. In this paper, we introduce a method for calculating this measure for the ith order statistic. We study the changes of the varentropy versus i for some distributions and show that in the symmetric distributions, under certain conditions, the median of the order statistics has minimum varentropy. Also, we introduce a new stochastic order based on the varentropy and relationships of it with the other stochastic orders.

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