J-measure of uncertainty (JMU) for specified probability distribution (1905.11955v1)

Abstract: In this paper it is shown that in the case of the given probability distribution or histogram using the Jaynes entropy maximum principle an J- measure of uncertainty (JMU) provides the maximum for a given distribution can be constructed. Formulas for the introduced JMU were obtained explicitly and calculations of this new measure for a number of distributions are shown as examples. It is shown using as the example a two-dimensional random variable, the application of the proposed method to the JMU estimation for the multidimensional case. It was made a comparison of the information contained in the histogram of a random variable with the information in the probability distribution obtained as a fitting of this histogram. Moreover studied the influence of an additional measurement of a certain physical quantity on the amount of information.