Related papers: Prediction of components in random sums
The often debated issue of `ratios of small numbers of events' is approached from a probabilistic perspective, making a clear distinction between the predictive problem (forecasting numbers of events we might count under well stated…
The problem of guessing subject to distortion is considered, and the performance of randomized guessing strategies is investigated. A one-shot achievability bound on the guessing moment (i.e., moment of the number of required queries) is…
Estimates are constructed for the deviation of the concentration functions of sums of independent random variables with finite variances from the folded normal distribution function without any assumptions concerning the existence of the…
In this paper the generalization of the Poisson distribution is derived for the case when each consecutive event changes event rate. A simple formula for the probability of observing of a given number of events for the selected period of…
In practice functional data are sampled on a discrete set of observation points and often susceptible to noise. We consider in this paper the setting where such data are used as explanatory variables in a regression problem. If the primary…
We examine the issue of stability of probability in reasoning about complex systems with uncertainty in structure. Normally, propositions are viewed as probability functions on an abstract random graph where it is implicitly assumed that…
This paper introduces inductive randomness predictors, which form a proper superset of inductive conformal predictors but have the same principal property of validity under the assumption of randomness (i.e., of IID data). It turns out that…
In this paper, two parametric probability distributions capable to describe the statistics of X-ray photon detection by a CCD are presented. They are formulated from simple models that account for the pile-up phenomenon, in which two or…
For a stochastic process reset at random times, we discuss to what extent the probabilities of some orderings of observables associated with the intervals of time between resetting events are universal, i.e., independent of the choice of…
In actuarial practice, the usual independence assumptions for the collective risk model are often violated, implying a growing need for considering more general models that incorporate dependence. To this purpose, the present paper studies…
In classical statistics and distribution testing, it is often assumed that elements can be sampled from some distribution $P$, and that when an element $x$ is sampled, the probability $P$ of sampling $x$ is also known. Recent work in…
Items in a test are often used as a basis for making decisions and such tests are therefore required to have good psychometric properties, like unidimensionality. In many cases the sum score is used in combination with a threshold to decide…
We propose and analyze a generalized splitting method to sample approximately from a distribution conditional on the occurrence of a rare event. This has important applications in a variety of contexts in operations research, engineering,…
Faced with massive data, subsampling is a commonly used technique to improve computational efficiency, and using nonuniform subsampling probabilities is an effective approach to improve estimation efficiency. For computational efficiency,…
The generalized Poisson distribution is well known to be a compound Poisson distribution with Borel summands. As a generalization we present closed formulas for compound Bartlett and Delaporte distributions with Borel summands and a…
The paper develops new methods of non-parametric estimation a compound Poisson distribution. Such a problem arise, in particular, in the inference of a Levy process recorded at equidistant time intervals. Our key estimator is based on…
Context: Software engineering has a problem in that when we empirically evaluate competing prediction systems we obtain conflicting results. Objective: To reduce the inconsistency amongst validation study results and provide a more formal…
We propose results of the investigation of properties of the random sums of random variables. We consider the case, where the number of summands is the first moment of an event occurrence. An integral equation is presented that determines…
In this chapter we review some examples, methods, and recent results involving comparison of clustering properties of point processes. Our approach is founded on some basic observations allowing us to consider void probabilities and moment…
The aim of the dissertation is threefold: the first two parts are devoted to explore the Fourth Moment Theorem and universality properties for homogeneous sums, while the last part approaches the classical theory of orthogonal polynomials…