Estimating the parameters of a nonhomogeneous Poisson process with linear rate

Estimating the parameters of a nonhomogeneous Poisson process with linear rate

Motivated by telecommunication applications, we investigate ways to estimate the parameters of a nonhomogeneous Poisson process with linear rate over a finite interval, based on the number of counts in measurement subintervals. Such a linear arrival-rate function can serve as a component of a piecewise-linear approximation to a general arrival-rate function. We consider ordinary least squares (...

Estimating the parameters of a seasonal Markov-modulated Poisson process

ESTIMATING THE PARAMETERS OF A FUZZY LINEAR REGRESSION MODEL

Fuzzy linear regression models are used to obtain an appropriate linear relation between a dependent variable and several independent variables in a fuzzy environment. Several methods for evaluating fuzzy coefficients in linear regression models have been proposed. The first attempts at estimating the parameters of a fuzzy regression model used mathematical programming methods. In this the...

Detecting Network Intrusion Using a Markov Modulated Nonhomogeneous Poisson Process

Network intrusion occurs when a criminal gains access to a customer's telephone, computer, bank, or other type of account. Detecting network intrusion is an important problem that has received little attention in the statistics literature. This article proposes a Markov modulated nonhomogeneous Poisson process (MMNHPP) to monitor transactions on a customer's account for deviations from the cust...

Generating Nonhomogeneous Poisson Processes

We present an overview of existing methods to generate pseudorandom numbers from a nonhomogeneous Poisson process. We start with various definitions of the nonhomogeneous Poisson process, present theoretical results (sometimes with a proof) that form the basis of existing generation algorithms, and provide algorithm listings. Whenever available, we also provide links to sources containing compu...