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...

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...

We present a general framework, the coupled compound Poisson factorization (CCPF), to capture the missing-data mechanism in extremely sparse data sets by coupling a hierarchical Poisson factorization with an arbitrary data-generating model. We derive a stochastic variational inference algorithm for the resulting model and, as examples of our framework, implement three different data-generating ...

In clinical and observational studies, recurrent event data (e.g., hospitalization) with a terminal event (e.g., death) are often encountered. In many instances, the terminal event is strongly correlated with the recurrent event process. In this article, we propose a semiparametric method to jointly model the recurrent and terminal event processes. The dependence is modeled by a shared gamma fr...

C-control chart assumes that process nonconformities follow a Poisson distribution. In actuality, however, this Poisson distribution does not always occur. A process control for semiconductor based on a Poisson distribution always underestimates the true average amount of nonconformities and the process variance. Quality is described more accurately if a compound Poisson process is used for pro...

C-control chart assumes that process nonconformities follow a Poisson distribution. In actuality, however, this Poisson distribution does not always occur. A process control for semiconductor based on a Poisson distribution always underestimates the true average amount of nonconformities and the process variance. Quality is described more accurately if a compound Poisson process is used for pro...

All current phylogenetic methods assume that DNA substitutions are independent among sites. However, ample empirical evidence suggests that the process of substitution is not independent but is, in fact, temporally and spatially correlated. The robustness of several commonly used phylogenetic methods to the assumption of independent substitution is examined. A compound Poisson process is used t...

OBJECTIVE to investigate the prevalence and factors associated with frailty in non-institutionalized older adults living in northern Minas Gerais, Brazil. METHOD data were collected in their homes, in 2013, based on a census cluster sampling. Demographic and socioeconomic variables, morbidities, utilization of health care services, and scores on the Edmonton Fragility Scale were analyzed. The...