Inferences Based on Burg Entropy Measures

Burg entropy, developed by John P. Burg in maximum entropy spectrum analysis, has inspired significant advancements in information theory. Expanding upon the cumulative residual Burg entropy, we present the concept of cumulative past Burg entropy and establish four characterisations of symmetric distributions. A characterisation result is used to provide a goodness‐of‐fit test for symmetry, demonstrating robust power and competitiveness with established methods available in the literature. We additionally offer a comprehensive Burg entropy characterisation of the uniform distribution and formulate a general theory that delineates distributions like the truncated exponential and truncated normal under appropriate conditions. We demonstrate that the dual of the modified Burg entropy aligns with positively scaled extropy and establish that, within the skew‐normal family, it reaches its maximum at the standard normal distribution.