Semi-Selfdecomposable Laws in the Minimum Scheme

We discuss semi-selfdecomposable laws in the minimum scheme and characterize them using an autoregressive model. Semi-Pareto and semi-Weibull laws of Pillai (1991) are shown to be semi-selfdecomposable in this scheme. Methods for deriving this class of laws are then attempted from the angle of randomization. Finally, discrete analogues of these results are also considered.