type="main" xml:id="jtsa12054-abs-0001" <p>We present an elaboration of the usual binomial AR(1) process on {0,1, … ,N}that allows the thinning probabilities to depend on the current state N only through the ‘density’ n ∕ N, a natural assumption in many real contexts. We derive some...</p>

This paper contains a survey of results related to quasi-stationary distributions, which arise in the setting of stochastic dynamical systems that eventually evanesce, and which may be useful in describing the long-term behaviour of such systems before evanescence. We are concerned mainly with...

Abstract Companies in business and industry often make very different demands on statistical software packages, like flexibility concerning customized solutions, possibility of integrating non-standard stochastic approaches, use to validated applications, user-friendly interface, moderate costs,...

The Poisson distribution is a simple and popular model for count-data random variables, but it suffers from the equidispersion requirement, which is often not met in practice. While models for overdispersed counts have been discussed intensively in the literature, the opposite phenomenon,...

The innovations of an INAR(1) process (<italic>in</italic>teger-valued <italic>a</italic>uto<italic>r</italic>egressive) are usually assumed to be unobservable. There are, however, situations in practice, where also the innovations can be uncovered, i.e. where we are concerned with a <italic>fully observed INAR<roman>(<italic>1</italic>)</roman> process</italic>. We analyze stochastic...