Laplace Transform Characterizations for Classes of Life Distributions

Characterization problems, in general, hold a special place in probability literature. The present paper, inspired by the seminal works of Vinogradov (Theory Probab Appl 18:811–813, 1974) and Block and Savits (Ann Probab 465–474, 1980), focuses on using the Laplace transform to obtain characterization results for certain classes of life distributions. We also highlight an interesting interpretation of such characterization results in terms of a specific type of shock model and also their potential applications in establishing results involving convolutions.