Abstract <p>This study extends the definitions of the generalized Student distributions to a wider range of distribution parameters and presents multiplication theorems that allow the generalized Student and Lomax distributions to be represented as scaled mixtures of the same distributions but with larger parameters. A similar result has been obtained for beta distributions. Analogs of multiplication theorems for the classical Student and Lomax distributions have been obtained as corollaries. Specifically, it has been shown that the Student distribution can be represented as a scaled mixture of the Student distribution with a larger number of degrees of freedom. Also, a representation of strictly stable distributions concentrated on the positive semiaxis has been obtained as scaled mixtures of a special distribution that is not stable. This alternative representation complements the multiplication theorem for these strictly stable laws.</p>