Families of distributions characterized by entropy
In this correspondence, we examine the relation between two random variables with common entropy function. The entropy has been used to measure dispersion, uncertainty, risk, and volatility, There is no general relationship between two random variables having equal entropies. We present results that identify certain conditions based on the entropy under which two random variables are stochastically equal, We also obtain similar results for the relative entropy.
entropy relative entropy convex ordering exponential distribution harmonic new better than used harmonic new worse than used increasing convex ordering stochastic ordering