In this paper, we propose a customer-arrival-based insurance risk model, in which customers’ potential claims are described as independent and identically distributed heavy-tailed randomvariables andpremiumsare the same for eachpolicy. Weobtain some precise large deviation results for the prospective-loss process under a mild assumption on the random index (in our case, the customer-arrival pro...

Let (X 1 ; X 2) be an-stable random vector, not necessarily symmetric, with 0 < < 2. The paper investigates the regression E(X 2 jX 1 = x) for all values of. We give conditions for the existence of the conditional moment E(jX 2 j p jX 1 = x) when p , and we obtain an explicit form of the regression E(X 2 jX 1 = x) as a function of x. Although this regression is, in general, not linear, it can b...

We extend a result of Dubins (Ann Probab 3:89–99, 1975) from bounded to unbounded random variables. Dubins showed that a finitely additive expectation over the collection of bounded random variables can be written as an integral of conditional expectations (disintegrability) if and only if the marginal expectation is always within the smallest closed interval containing the conditional expectat...

 The evaluation of uncertainties according to the „„Guide to the Expression of Uncertainty in Measurement‟‟ is presented in this study based on a novel Fuzzy-randomvariables approach. Whereas the classically proposed methods like Monte Carlo techniques treat all uncertainties as having a random nature, the fuzzy technique distinguishes between aleatoric and epistemic uncertainties. The aleator...

Carcinogenesis, as every biological process, is not purely deterministic since all systems are subject to random perturbations from the environment. In tumor growth models, the values of the parameters are subject to many uncertainties that can arise from experimental variations or due to patient-specific data. The present work is devoted to the development and analysis of numerical methods for...

In most statistical analysis, inequality or extent of variation in income isrepresented in terms of certain summary measures. But some authors arguedthat the concept of inequality is vague and thus cannot be measured as anexact concept. Therefore, fuzzy set theory provides naturally a useful toolfor such circumstances. In this paper we have introduced a real-valued fuzzymethod of illustrating t...

Inmany applications, the cumulative distribution function (cdf) FQN of a positively weighted sum of N i.i.d. chi-squared randomvariables QN is required.Although there is no known closed-form solution for FQN , there are many good approximations. When computational efficiency is not an issue, Imhof’smethod provides a good solution. However, when both the accuracy of the approximation and the spe...

Klaus Schmidt proved that if a strictly stationary sequence of (say) real-valued random variables is such that the family of distributions of its partial sums is tight, then that sequence is a \coboundary". Here Schmidt's result is extended to some (not necessarily stationary) sequences of random variables taking their values in a separable real Banach space.

Computational processmodels in combinationwith innovative designmethodologies provide a powerful reactor design platform. Yet, model-based design is mostly done in a pure deterministic way. Possible uncertainties of the underlying model parameters, prediction errors due to simplifying assumptions regarding the reactor behavior and suboptimal realizations of the design along the reaction coordin...