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We study different fractional extensions of the Poisson process and generalized counting processes by introducing time-change represented by the inverse to the sums of stable and tempered stable subordinators. We state the governing…
This paper considers a model with general regressors and unobservable factors. An estimator based on iterated principal components is proposed, which is shown to be not only asymptotically normal and oracle efficient, but under certain…
We present a structured additive regression approach to model conditional densities given scalar covariates, where only samples of the conditional distributions are observed. This links our approach to distributional regression models for…
Sufficient conditions are developed for a class of generalized Polya urn schemes ensuring exchangeability. The extended class includes the Blackwell-MacQueen Polya urn and the urn schemes for the two-parameter Poisson-Dirichlet process and…
This paper investigates asymptotic estimates for the entrance probability of the discounted aggregate claim vector from a multivariate renewal risk model into some rare set. We provide asymptotic results for the entrance probability on both…
The processes of the averaged regression quantiles and of their modifications provide useful tools in the regression models when the covariates are not fully under our control. As an application we mention the probabilistic risk assessment…
In biomedical studies, we are often interested in the association between different types of covariates and the times to disease events. Because the relationship between the covariates and event times is often complex, standard survival…
Inspired by recent work of Alberts, Khanin and Quastel, we formulate general conditions ensuring that a sequence of multi-linear polynomials of independent random variables (called polynomial chaos expansions) converges to a limiting random…
This study considers the Merton model with temporal correlation. We show the Merton model becomes Poisson process with the log-normal distributed intensity function in the limit. We discuss the relation between this model and Hawkes…
We obtain an asymptotic normality result that reveals the precise asymptotic behavior of the maximum likelihood estimators of parameters for a very general class of linear mixed models containing cross random effects. In achieving the…
Multivariate Poisson processes have many important applications in Insurance, Finance, and many other areas of Applied Probability. In this paper we study the backward simulation approach to modelling multivariate Poisson processes and…
The binomial, the negative binomial, the Poisson, the compound Poisson and the Erlang distribution do all admit integral representations with respect to its (continuous) parameter. We use the Margulis-Russo type formulas for Bernoulli and…
We consider a parametric modelling approach for survival data where covariates are allowed to enter the model through multiple distributional parameters, i.e., scale and shape. This is in contrast with the standard convention of having a…
This article develops an analytical framework for studying information divergences and likelihood ratios associated with Poisson processes and point patterns on general measurable spaces. The main results include explicit analytical…
The contact process and the slightly different susceptible-infected-susceptible model are studied on long-range connected networks in the presence of random transition rates by means of a strong disorder renormalization group method and…
We generalize the Poisson limit theorem to binary functions of random objects whose law is invariant under the action of an amenable group. Examples include stationary random fields, exchangeable sequences, and exchangeable graphs. A…
This paper studies new Lancaster characterizations of bivariate multivariate Poisson, negative binomial and normal distributions which have diagonal expansions in multivariate orthogonal polynomials. The characterizations extend classical…
In this paper, we study a multivariate version of the generalized counting process (GCP) and discuss its various time-changed variants. The time is changed using random processes such as the stable subordinator, inverse stable subordinator,…
We develop nonparametric Bayesian modelling approaches for Poisson processes, using weighted combinations of structured beta densities to represent the point process intensity function. For a regular spatial domain, such as the unit square,…
A validated simulation model primarily requires performing an appropriate input analysis mainly by determining the behavior of real-world processes using probability distributions. In many practical cases, probability distributions of the…