This article considers the problem of evaluating infinite-time (or finite-time) ruin probability under a given compound Poisson surplus process by approximating the claim size distribution by a finite mixture exponential, say Hyperexponential, distribution. It restates the infinite-time (or finite-time) ruin probability as a solvable ordinary differential equation (or a partial differential equ...

Non-negative matrix factorization models based on a hierarchical Gamma-Poisson structure capture user and item behavior effectively in extremely sparse data sets, making them the ideal choice for collaborative filtering applications. Hierarchical Poisson factorization (HPF) in particular has proved successful for scalable recommendation systems with extreme sparsity. HPF, however, suffers from ...

in the analysis of spatial point patterns, complete spatial randomness (csr) hypothesis,which is a restriction of a homogenous poisson process to study region a, operates as a dividinghypothesis between “regular” and “aggregated” patterns. meanwhile, many alternatives to csr inaggregated patterns are extensions of homogenous poisson processes themselves. therefore, when thecsr hypothesis is rej...

Multiplicative processes and multifractals proved useful in various applications ranging from hydrodynamic turbulence to computer network traffic. Placing multifractal analysis in the more general framework of infinitely divisible laws, we design processes which possess at the same time stationary increments as well as multifractal and more general infinitely divisible scaling over a continuous...

In compound Poisson disorder problem, arrival rate and/or jump distribution of some compound Poisson process change suddenly at some unknown and unobservable time. The problem is to detect the change (or disorder) time as quickly as possible. A sudden regime-shift may require some counter-measures be taken promptly, and a quickest detection rule can help with those efforts. We describe complete...

We study the quantization problem for certain types of jump processes. The probabilities for the number of jumps are assumed to be bounded by Poisson weights. Otherwise, jump positions and increments can be rather generally distributed and correlated. We show in particular that in many cases entropy coding error and quantization error have distinct rates. Finally, we investigate the quantizatio...