Most non-homogenous Poisson process (NHPP) based software reliability growth models (SRGMs) presented in the literature assume that the faults in the software are of the same type. This assumption implies that the fault removal rate per remaining faults is independent of the testing time. However, this assumption is not truly representative of reality. It has been observed that the software con...

Non-homogenous Poisson processes with periodic claim intensity rate are proposed as the claim counting process of risk theory. We introduce a doubly periodic Poisson model with short and long term trends, illustrated by a double-beta intensity function. Here periodicity does not repeat the exact same short term pattern every year, but lets its peak intensity vary over a longer period. This mode...

Let N , N1 and N2 be point processes such that N1 is obtained from N by homogeneous independent thinning and N2 = N −N1. We give a new elementary proof that N1 and N2 are independent if and only if N is a Poisson point process. We present some applications of this result to test if a homogeneous point process is a Poisson point process.

Neural information is characterized by sets of spiking events that travel within the brain through neuron junctions that receive, transmit, and process streams of spikes. Coincidence detection is one of the ways to describe the functionality of a single neural cell. This letter presents an analytical derivation of the output stochastic behavior of a coincidence detector (CD) cell whose stochast...

Given a homogeneous Poisson process on R with intensity λ, we prove that it is possible to partition the points into two sets, as a deterministic function of the process, and in an isometry-equivariant way, so that each set of points forms a homogeneous Poisson process, with any given pair of intensities summing to λ. In particular, this answers a question of Ball [3], who proved that in d = 1,...

We present an overview of existing methods to generate pseudorandom numbers from homogeneous Poisson processes. We provide three well-known definitions of the homogeneous Poisson process, present results that form the basis of various existing generation algorithms, and provide algorithm listings. With the intent of guiding users seeking an appropriate algorithm for a given setting, we note the...