ON THE MAXIMUM-ENTROPY DISTRIBUTION ON [0, ∞) WITH GIVEN FIRST TWO MOMENTS

Abstract

We are concerned with the maximum-entropy distribution on [0, ∞) with given mean m₁ and second moment m₂. For the case where m₂≤2m₁², we describe an algorithm for calculating the maximum-entropy distribution. In this case, if m₂→ m₁², the maximum-entropy distribution approaches the unit distribution degenerated at m₁, and if m²=2m₁² then the maximum-entropy distribution is the exponential distribution. For the other case where m₂>2m₁², we will show that there exists no maximumentropy distribution.