Normal distribution based on maximum Deng entropy

We define the distribution of uncertainty based on Deng entropy and proved that the limiting form of the distribution is the normal distribution by the characteristic function. We conduct some discussion on the distribution, and we further analyze the error of its normal approximation and give the conditions that should be satisfied for the requirement of given error. Finally, we reveal the relationship between the distribution and the binomial distribution and the advantages of taking it as a prior distribution in evidence theory.

Automated summary

We define the distribution of uncertainty using Deng entropy and prove its limiting form to be the normal distribution through the characteristic function. We discuss the distribution, analyze the error of its normal approximation, and provide conditions for required error. Furthermore, we reveal the relationship between the distribution and the binomial distribution, highlighting the advantages of using it as a prior distribution in evidence theory.