Branching processes are a class of continuous-time Markov chains (CTMCs) with ubiquitous applications. A general difficulty in statistical inference under partially observed CTMC models arises in computing transition probabilities when the discrete state space is large or uncountable. Classical methods such as matrix exponentiation are infeasible for large or countably infinite state spaces, an...

Let (Xn) be a sequence of independent and identically distributed random variables, with common absolutely continuous distribution F . An observation Xn is a near-record if Xn ∈ (Mn−1 − a, Mn−1], where Mn = max{X1, . . . , Xn} and a > 0 is a parameter. We analyze the point process η on [0,∞) of near-record values from (Xn), showing that it is a Poisson cluster process. We derive the probability...

We assess the performance of a discrete-time queueing system with train arrivals. Arrivals at the queue stem from a number of active sessions, each generating a packet in a slot with fixed probability q. Since an exact analysis is not feasible for q 6= 1, we rely on Taylor-series expansions around q = 0 of the joint probability generating functions of the number of active sessions and the queue...

We consider a discrete-time infinite-capacity queueing system with a general uncorrelated arrival process, constant-length service times of multiple slots, multiple servers and a first-come-first-served queueing discipline. Under the assumption that the queueing system can reach a steady state, we first establish a relationship between the steady-state probability distributions of the system co...

Branching processes are a class of continuous-time Markov chains (CTMCs) with ubiquitous applications. A general difficulty in statistical inference under partially observed CTMC models arises in computing transition probabilities when the discrete state space is large or uncountable. Classical methods such as matrix exponentiation are infeasible for large or countably infinite state spaces, an...

For each distribution, I give the name of the distribution along with one or two parameters and indicate whether it is a discrete distribution or a continuous one. Then I describe an example interpretation for a random variable X having that distribution. Each discrete distribution is determined by a probability mass function f which gives the probabilities for the various outcomes, so that f(x...

For each distribution, I give the name of the distribution along with one or two parameters and indicate whether it is a discrete distribution or a continuous one. Then I describe an example interpretation for a random variable X having that distribution. Each discrete distribution is determined by a probability mass function f which gives the probabilities for the various outcomes, so that f(x...

This paper presents the analysis of outage probability for a cooperative diversity wireless network using amplify-and-forward relays over independent non-identical distributed Weibull and Weibull-lognormal fading channels for single as well as multiple relays. To reach that end, a closed-from expression for the moment-generating function of the total signal-to-noise-ratio (SNR) at the destinati...

The Ziggurat Algorithm is a very fast rejection sampling method for generating PseudoRandom Numbers (PRNs) from statistical distributions. In the algorithm, rectangular sampling domains are layered on top of each other (resembling a ziggurat) to encapsulate the desired probability density function. Random values within these layers are sampled and then returned if they lie beneath the graph of ...

 Abstract—In this paper, we consider the analysis of cooperative relay-based amplify-and-forward system in terms of Shannon capacity, probability of error, and outage probability over fading channels. The relay gain is optimized with the objective of maximizing the received signal-to-noiseratio (SNR) at the destination, given that the fading statistics of the links in the cooperative system ar...