By dealing with interarrival times as exponentially distributed fuzzy random variables, a fuzzy random homogeneous Poisson process and a fuzzy random compound Poisson process are respectively defined. Several theorems on the two processes are provided, respectively.

In this paper, we introduce and study a convoluted version of the time fractional Poisson process by taking discrete convolution with respect to space variable in system differential equations that governs its state probabilities. We call introduced as (CFPP). The explicit expression for Laplace transform probabilities are obtained whose inversion yields one-dimensional distribution. Some stati...

In [1], a new coverage process was defined. It was motivated by the various SINR(Signal to Interference Noise Ratio) models in wireless communications. The underlying point process was assumed to be a Poisson process. In this report, we extend the theory to the case when the underlying point process is a Poisson-Poisson cluster process. Firstly, we define the stochastic geometric model. We give...

We introduce a probabilistic model for the factorisation of continuous Poisson process rate functions. Our model can be thought of as a topic model for Poisson point processes in which each point is assigned to one of a set of latent rate functions that are shared across multiple outputs. We show that the model brings a means of incorporating structure in point process inference beyond the stat...

Compound Poisson processes are often useful as approximate models, when describing the occurrence of rare events. In this paper, we develop a method for showing how close such approximations are. Our approach is to use Stein's method directly, rather than by way of declumping and a marked Poisson process; this has conceptual advantages, but entails technical difficulties. Several applications a...