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51.
Harold Graboyes Elvin L. Anderson Sidney H. Levinson Theodore M. Resnick 《Journal of heterocyclic chemistry》1975,12(6):1225-1231
A general synthesis of acridines has been developed using diphenylamine-2-carboxaldehydes. Diphenylamine-2-carboxylic acids are converted to their p-toluenesulfonylhydrazides which are decomposed using a modified McFadyen-Stevens reaction to yield an aldehyde derivative which affords the acridine upon treatment with mineral acid. 相似文献
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Smoothing the Moment Estimator of the Extreme Value Parameter 总被引:1,自引:0,他引:1
Let {X
n be a sequence of i.i.d. random variables whose common distribution F belongs to the domain of attraction of an extreme value law. A semi-parametric estimator of the extreme value parameter is the Dekkers, Einmahl and de Haan [8] moment estimator. Practical use of this estimator requires the problematic choice of a number k=k(n) of upper order statistics and there are few reliable guidelines for this choice. An averaging or smoothing technique is proposed for this estimator yielding a less volatile function of k which in practice aids estimation. 相似文献
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For integers n ≥ r, we treat the rth largest of a sample of size n as an \(\mathbb {R}^{\infty }\)-valued stochastic process in r which we denote as M(r). We show that the sequence regarded in this way satisfies the Markov property. We go on to study the asymptotic behavior of M(r) as r → ∞, and, borrowing from classical extreme value theory, show that left-tail domain of attraction conditions on the underlying distribution of the sample guarantee weak limits for both the range of M(r) and M(r) itself, after norming and centering. In continuous time, an analogous process Y(r) based on a two-dimensional Poisson process on \(\mathbb {R}_{+}\times \mathbb {R}\) is treated similarly, but we note that the continuous time problems have a distinctive additional feature: there are always infinitely many points below the rth highest point up to time t for any t >?0. This necessitates a different approach to the asymptotics in this case. 相似文献
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