The authors present evidence for universality in numerical computations with random data. Given a (possibly stochastic) numerical algorithm with random input data, the time (or number of iterations) to convergence (within a given tolerance) is a random variable, called the halting time. Two-component universality is observed for the fluctuations of the halting time--i.e., the histogram for the ...

Guidorzi has now written two papers (astro-ph/0507588 and astro-ph/0508483, both accepted to MNRAS) on the GRB variability-luminosity correlation in which he finds that expanded samples of L vs. V data are not well described by a power law because the scatter of the data around such a model is more than can be accounted for by the data’s statistical errors alone (sample variance) – “in contrast...

Many studies aim to assess whether a therapy has a beneficial effect on multiple outcomes simultaneously relative to a control. Often the joint null hypothesis of no difference for the set of outcomes is tested using separate tests with a correction for multiple tests, or using a multivariate T2-like MANOVA or global test. However, a more powerful test in this case is a multivariate one-sided o...

In many practical situations, we do not know the shape of the corresponding probability distributions and therefore, we need to use robust statistical techniques, i.e., techniques that are applicable to all possible distributions. Empirically, it turns out the the most efficient robust version of sample variance is the average value of the p-th powers of the deviations |xi − â| from the (estima...

Several representations of the exact cdf of the sum of squares of n independent identically gamma–distributed random variables Xi are given, in particular by a series of gamma distribution functions. Using a characterization of the gamma distribution by Laha, an expansion of the exact distribution of the sample variance is derived by a Taylor series approach with the former distribution as its ...

In this paper we construct high moment partial sum processes based on residuals of a GARCH model when the mean is known to be 0. We consider partial sums of kth powers of residuals, CUSUM processes and self-normalized partial sum processes. The kth power partial sum process converges to a Brownian process plus a correction term, where the correction term depends on the kth moment μk of the inno...

Nationally representative samples of large populations often have complex design features for a variety of reasons (e.g., cost efficiency). For purposes of estimating sampling variances based on complex multi-stage sample designs involving stratification and cluster sampling, the sampling error codes provided by survey organizations in public use survey data files often assume “ultimate cluster...