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Recent advances in computation technology for decision/simulation and uncertainty analyses have revived interest in the triangular distribution and its use to describe uncertainty of bounded input phenomena. The trapezoidal distribution is a generalization of the triangular distribution that allows for the specification of the modal value by means of a range of values rather than a single point estimate. Whereas the trapezoidal and the triangular distributions are restricted to linear geometric forms in the successive stages of the distribution, the generalized trapezoidal (GT) distribution allows for a nonlinear behavior at its tails and a linear incline (or decline) in the central stage. In this paper we develop two novel elicitation procedures for the parameters of a special case of the GT family by restricting ourselves to a uniform (horizontal) central stage in accordance with the central stage of the original trapezoidal distribution. [ABSTRACT FROM AUTHOR]

In this paper, we derive the asymptotic distributions of AugmentedDickey-Fuller (ADF) tests under very mild conditions. The tests were originally proposed and investigated by Said and Dickey (1984) for testing unit roots in finite-order ARMA models with i.i.d, innovations, and are based on a finite AR process of order increasing with the sample size. Our conditions are significantly weaker than theirs. In particular, we allow for general linear processes with martingale difference innovations, possibly having conditional heteroskedasticities. The linear processes driven by ARCH type innovations are thus permitted. The range for the permissible increasing rates for the AR approximation order is also much wider. For the usual t-type test, we only require that it increase at order o(n[sup ½]) while they assume that it is of order o(n[sub K]) for some k satisfying 0 < k ≤ 1/3. [ABSTRACT FROM AUTHOR]

This paper comments on a recent paper by R. Rhouma and B. Safya [Chaos 17, 033117 (2007)]. They claimed to find some security weakness of the spatiotemporal chaotic cryptosystem suggested by G. Tang et al. [Phys. Lett. A 318, 388 (2003)] and proposed a chosen-plaintext attack to analyze this system. We find that in their analysis, called a “chosen-plaintext attack,” they actually act as a legal receiver (with a machine in their hands during the entire decryption process) rather than an attacker and, therefore, the whole reasoning is not valid. [ABSTRACT FROM AUTHOR]