Showing papers by "Antonio Di Crescenzo published in 2009"

On Cumulative Entropies and Lifetime Estimations

Abstract: The cumulative entropy is a new measure of information, alternative to the classical differential entropy. It has been recently proposed in analogy with the cumulative residual entropy studied by Wang et al. (2003a) and (2003b). After recalling its main properties, including a connection to reliability theory, we discuss estimates of random lifetimes based on the empirical cumulative entropy, which is suitably expressed in terms of the dual normalized sample spacings.

On a Symmetric, Nonlinear Birth-Death Process with Bimodal Transition Probabilities

Abstract: We consider a bilateral birth-death process having sigmoidal-type rates. A thorough discussion on its transient behaviour is given, which includes studying symmetry properties of the transition probabilities, finding conditions leading to their bimodality, determining mean and variance of the process, and analyzing absorption problems in the presence of 1 or 2 boundaries. In particular, thanks to the symmetry properties we obtain the avoiding transition probabilities in the presence of a pair of absorbing boundaries, expressed as a series.

On a first-passage-time problem for the compound power-law process

Abstract: We consider a first-passage-time problem for a compound Poisson process characterized by independent, identically and exponentially distributed jumps, occurring according to the power-law process (PLP). First of all, we refer to the conditional product moments of arrival times and to the interarrival times density of a power-law process. We then obtain the probability density of the crossing time through a linear boundary at the occurrence of the nth jump. In particular, we express the first-passage-time density in terms of a conditional expectation involving the arrival times.

A Neuronal Model with Excitatory and Inhibitory Inputs Governed by a Birth-Death Process

Abstract: A stochastic model for the firing activity of a neuronal unit has been recently proposed in [4]. It includes the decay effect of the membrane potential in the absence of stimuli, and the occurrence of excitatory inputs driven by a Poisson process. In order to add the effects of inhibitory stimuli, we now propose a Stein-type model based on a suitable exponential transformation of a bilateral birth-death process on ${\mathbb Z}$ and characterized by state-dependent nonlinear birth and death rates. We perform an analysis of the probability distribution of the stochastic process describing the membrane potential and make use of a simulation-based approach to obtain some results on the firing density.