In spiral ganglion neurons (SGNs), the afferent single units of the auditory nerve, high spontaneous and evoked firing rates ensure preservation of the temporal code describing the key features of incoming sound. During postnatal development, the spatiotemporal distribution of ion channel subtypes contributes to the maturation of action potential generation in SGNs, and to their ability to gene...

A sequence of first–order integer–valued autoregressive type (INAR(1)) processes is investigated, where the autoregressive type coefficients converge to 1. It is shown that the limiting distribution of the joint conditional least squares estimators for this coefficient and for the mean of the innovation is normal. Consequences for sequences of Galton–Watson branching processes with unobservable...

Several pieces of research have spotlighted the importance count data modelling and its applications in real-world phenomena. In light this, a novel two-parameter compound-Poisson distribution is developed this paper. Its mathematical functionalities are investigated. The two unknown parameters estimated using both maximum likelihood Bayesian approaches. We also offer parametric regression mode...

This paper focuses on different methods of estimation and forecasting in first-order integer-valued autoregressive processes with Poisson-Lindley (PLINAR(1)) marginal distribution. For this purpose, the parameters of the model are estimated using Whittle, maximum empirical likelihood and sieve bootstrap methods. Moreover, Bayesian and sieve bootstrap forecasting methods are proposed and predict...

and Applied Analysis 3 the autoregressive coefficient estimator. For the nonstationary of continuous-valued time series, we often need to examine whether the characteristic polynomial of AR(1) process has a unit root. Thus, we want to see if we can find the limiting distribution of the autoregressive coefficient estimator. Let us present a result that is needed later on. Lemma 3. Suppose that Z...