This paper first recalls some stochastic orderings useful for studying the ℒ-class and the Laplace order in general. We use these orders to show that the higher moments of an ℒ-class distribution need not exist. Using simple sufficient conditions for the Laplace ordering, we give examples of distributions in the ℒ- and ℒα-classes. Moreover, we present explicit sharp bounds on the survival function of a distribution belonging to the ℒ-class of life distributions. The results reveal that the ℒ-class should not be seen as a more comprehensive class of ageing distributions but rather as a large class of life distributions on its own.
