Three classes of decomposable distributions

Abstract

In this work, we refine the results of Sendov and Shan [New representation theorems for completely monotone and Bernstein functions with convexity properties on their measures, J. Theor. Probab. 28 (2015), 1689–1725] on subordinators obtained by the class of Bernstein functions stable by the Mellin-Euler differential operator I−xddxI-x\tfrac{\text{d}}{\text{d}x} by giving a stochastic interpretation, proving monotonicity properties of the related distributions and providing additional extensions.

Keywords

• bernstein functions
• complete monotonicity
• concavity
• convexity
• infinite divisibility
• laplace transform
• mellin-euler differential operator
• stable distribution
• subordinators
• 60e07
• 60e15