Stretched exponential probability density functions (pdf), having the form of the exponential of minus a fractional power of the argument, are commonly found in turbulence and other areas. They can arise because of an underlying random multiplicative process. For this, a theory of extreme deviations is developed, devoted to the far tail of the pdf of the sum X of a finite number n of independen...

1 Probability distribution functions Probability distribution functions assign probabilities to each of the possible outcomes of a random experiment. These distributions can be continuous (e.g. grading on a 4.0 scale), or discrete (e.g. grading with letter grades) (see Fig. 2). Figure 1: Terminology for continuous and discrete probability distributions. A probability distribution function speci...

This appendix explains the procedure for developing the pdf for climate sensitivity. The study began by reviewing the five probability density functions for equilibrium climate sensitivity (ECS) used in the IPCC AR5 that draw upon multiple lines of evidence. These are Aldrin et al. (2012), Libardoni and Forest (2013), Olsen et al. (2012), Annan and Hargreaves (2006), and Hegerl et al. (2006). T...

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Stretched exponential probability density functions (pdf), having the form of the exponential of minus a fractional power of the argument, are commonly found in turbulence and other areas. They can arise because of an underlying random multiplicative process. For this, a theory of extreme deviations is developed, devoted to the far tail of the pdf of the sum X of a finite number n of independen...

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In this paper, we introduce a hierarchical anomaly network intrusion detection system, which is capable of detecting network–based attacks using statistical preprocessing models and neural network classification. The sample network used has a three-tier hierarchy, where the lower tier detectors report to the higher tiers. The statistical preprocessor converts network traffic sample information ...

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