  In R\'enyi's representation for exponential order statistics, we change the
iid exponential sequence to any iid sequence, and call the resulting order
statistic \emph{generalized R\'enyi statistic}. We prove that randomly
reordering the variables in the generalized R\'enyi statistic, in the limit we
obtain a sequence of iid exponentials. This result allows us to propose a new
model for heavy-tailed data. We investigate the problem of estimation of the
tail index in the new model.
