From the Publisher:
A valuable reference for the novice as well as for the expert who needs a wider scope of coverage within the area of cryptography, this book provides easy and rapid access of information and includes more than 200 algorithms and protocols; more than 200 tables and figures; more than 1,000 numbered definitions, facts, examples, notes, and remarks; and over 1,250 significant references, including brief comments on each paper.

Handbook of Applied Cryptography

Given C samples, with n i observations in the ith sample, a test of the hypothesis that the samples are from the same population may be made by ranking the observations from from 1 to Σn i (giving each observation in a group of ties the mean of the ranks tied for), finding the C sums of ranks, and computing a statistic H. Under the stated hypothesis, H is distributed approximately as χ2(C – 1), unless the samples are too small, in which case special approximations or exact tables are provided. One of the most important applications of the test is in detecting differences among the population means.* * Based in part on research supported by the Office of Naval Research at the Statistical Research Center, University of Chicago.

Use of Ranks in One-Criterion Variance Analysis

Value at Risk (VaR) has become the standard measure of market risk employed by financial institutions for both internal and regulatory purposes. VaR is defined as the value that a portfolio will lose with a given probability, over a certain time horizon (usually one or ten days). Despite its conceptual simplicity, its measurement is a very challenging statistical problem and none of the methodologies developed so far give satisfactory solutions. Interpreting the VaR as the quantile of future portfolio values conditional on current information, we propose a new approach to quantile estimation which does not require any of the extreme assumptions invoked by existing methodologies (such as normality or i.i.d. returns). The Conditional Autoregressive Value-at-Risk or CAViaR model moves the focus of attention from the distribution of returns directly to the behavior of the quantile. We specify the evolution of the quantile over time using a special type of autoregressive process and use the regression quantile framework introduced by Koenker and Bassett to determine the unknown parameters. Since the objective function is not differentiable, we use a differential evolutionary genetic algorithm for the numerical optimization. Utilizing the criterion that each period the probability of exceeding the VaR must be independent of all the past information, we introduce a new test of model adequacy, the Dynamic Quantile test. Applications to simulated and real data provide empirical support to this methodology and illustrate the ability of these algorithms to adapt to new risk environments.

/pdf/caviar-conditional-autoregressive-value-at-risk-by-2m5i5yark7.pdf

CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles *

Diversity, biotic and similarity indices: A review with special relevance to aquatic ecosystems

Multivariate generalizations of the Wald--Wolfowitz runs statistic and the Smirnov maximum deviation statistic for the two-sample problem are presented. They are based on the minimal spanning tree of the pooled sample points. Some null distribution results are derived and a simulation study of power is reported. 5 figures, 2 tables.

/pdf/multivariate-generalizations-of-the-wald-wolfowitz-and-4ngeuwokzx.pdf

Multivariate Generalizations of the Wald-Wolfowitz and Smirnov Two-Sample Tests

/pdf/the-distribution-theory-of-runs-52f6pvxky1.pdf

The Distribution Theory of Runs

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The Distribution Theory of Runs