  The generalized inverse Gaussian-Poisson (GIGP) distribution proposed by
Sichel in the 1970s has proved to be a flexible fitting tool for diverse
frequency data, collectively described using the item production model. In this
paper, we identify the limit shape (specified as an incomplete gamma function)
of the properly scaled diagrammatic representations of random samples from the
GIGP distribution (known as Young diagrams). We also show that fluctuations are
asymptotically normal and, moreover, the corresponding empirical random process
is approximated via a rescaled Brownian motion in inverted time, with the
inhomogeneous time scale determined by the limit shape. Here, the limit is
taken as the number of production sources is growing to infinity, coupled with
an intrinsic parameter regime ensuring that the mean number of items per source
is large. More precisely, for convergence to the limit shape to be valid, this
combined growth should be fast enough. In the opposite regime referred to as
"chaotic", the empirical random process is approximated by means of an
inhomogeneous Poisson process in inverted time. These results are illustrated
using both computer simulations and some classic data sets in informetrics.
