A relative entropy method to measure non-exponential random data

• A relative entropy method is developed to measure non-exponential random data.
• The fractional order moment, logarithmic moment and tail statistics are employed.
• The three strategies of Mittag–Leffler distribution can be accurately established.
• Compared with Shannon entropy, the relative entropy method is easy to be implemented.

This paper develops a relative entropy method to measure non-exponential random data in conjunction with fractional order moment, logarithmic moment and tail statistics of Mittag–Leffler distribution. The distribution of non-exponential random data follows neither the exponential distribution nor exponential decay. The proposed strategy is validated by analyzing the experiment data, which are generated by Monte Carlo method using Mittag–Leffler distribution. Compared with the traditional Shannon entropy, the relative entropy method is simple to be implemented, and its corresponding relative entropies approximated by the fractional order moment, logarithmic moment and tail statistics can easily and accurately detect the non-exponential random data.