1,721,015 research outputs found
Universal methods for generating random variables with a given characteristic function
No full textUniversal generators for absolutely-continuous and integer-valued random variables are introduced. The proposal is based on a generalization of the rejection technique proposed by Devroye [The computer generation of random variables with a given characteristic function. Computers and Mathematics with Applications. 1981;7:547–552]. The method involves a dominating function solely requiring the evaluation of integrals which depend on the characteristic function of the underlying random variable. The proposal gives rise to simple algorithms which may be implemented in a few code lines and which may show noticeable performance even if some classical families of distributions are considered
Discussion of “On simulation and properties of the stable law” by L. Devroye and L. James
No full textOn the Generalized Benford's law
No full textWe provide some properties of the Generalized Benford law – a flexible model for the distribution of significant digits – which accurately describes the pattern of leading digits in the sequences of prime numbers and of non-trivial Riemann zeta zeros. © 2020 Elsevier B.V
Skorohod representation on a given probability space
No full textLet be a probability space, a metricspace, a probability measure on the Borel -field of, and an arbitrary map,. If is tight and converges indistribution to (in Hoffmann-J\o rgensen's sense), then for some -valued random variable on. If, in addition, the aremeasurable and tight, there are -valued random variables and , defined on, such that , and a.s. forsome subsequence . Further, \overset{\sim}{X}_n\rightarrowX a.s. (without need of taking subsequences) if forall , or if for some and all . When isperfect, the tightness assumption can be weakened intoseparability up to extending to for some with . As a consequence, inapplying Skorohod representation theorem with separableprobability measures, the Skorohod space can be taken, for some with outer Lebesgue measure 1, where is theBorel -field on and the only extension ofLebesgue measure such that . In order to prove theprevious results, it is also shown that, if converges indistribution to a separable limit, then converges stablyfor some subsequence
Aggregation of not independent experts' opinions under ambiguity
No full textWe consider an aggregation scheme of opinions expressed through different probability distributions or multiple priors decision model. The decision-maker adopts entropy maximization as a measure of risk diversification and a rational form of prudence for valuing uncertain outcomes. We show a new aggregation rule based on the composite value function that is able to represent asymmetric attitude on extreme events (optimism with respect to windfall gains and pessimism with respect to catastrophic events) and a rational prudence on ordinary events. We define when the new rule preserves stochastic dominance
Two versions of the fundamental theorem of asset pricing
No full textLet be a convex cone of real random variables on the probability space . The existence of a probability on such that
egin{equation*}
Psim P_0,quad E_Pabs{X
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