Aperiodic pseudorandom number generators based on infinite words

In this paper we study how certain families of aperiodic infinite words can be used to produce aperiodic pseudorandom number generators (PRNGs) with good statistical behavior. We introduce the well distributed occurrences (WELLDOC) combinatorial property for infinite words, which guarantees absence of the lattice structure defect in related pseudorandom number generators. An infinite word u on a d-ary alphabet has the WELLDOC property if, for each factor w of u, positive integer m, and vector v in (Z_d)^m, there is an occurrence of w such that the Parikh vector of the prefix of u preceding such occurrence is congruent to v modulo m. (The Parikh vector of a finite word v over an alphabet A has its i-th component equal to the number of occurrences of the i-th letter of A in v.) We prove that Sturmian words, and more generally Arnoux–Rauzy words and some morphic images of them, have the WELLDOC property. Using the TestU01 and PractRand statistical tests, we moreover show that not only the lattice structure is absent, but also other important properties of PRNGs are improved when linear congruential generators are combined using infinite words having the WELLDOC property

Meta-análise : harmonização de testes usando os valores de prova

Tese de doutoramento, Estatística e Investigação Operacional (Probabilidades e Estatística), Universidade de Lisboa, Faculdade de Ciências, 2009Apresenta-se uma breve resenha de tópicos de Meta-Análise que mostram a importância dessa subdisciplina da Estatística na construção do conhecimento científico, viabilizando sínteses dos factos e conclusões conhecidas, e explora-se com algum detalhe o problema das sínteses usando níveis de significância descritivos. Apresentamos uma técnica artificiosa de calcular pseudo ps, ampliando computacionalmente a amostra, e estudamos as implicações desses procedimentos na potência dos testes meta-analíticos usuais, de Fisher e de Tippett; usando os métodos de Stoffer, averiguamos o impacto do uso da amostra ampliada no número de estudos não significativos que seriam necessários para virar a decisão de rejeição global, uma das formas mais usadas de avaliar o efeito do enviesamento na publicação nas revisões sistemáticas e sínteses meta-analíticas. Estabelecem-se ainda resultados sobre caracterização de uniformes, e estuda-se a distribuição exacta de funções de betas potencialmente úteis em eventuais extensões usando espaçamentos.We present a brief overview of the main topics in Meta-Analysis, enhancing its relevance towards scientific knowledge building, via syntheses of facts and conclusions of previous work. The main original contributions are in the special field of meta-analytical syntheses based on reported p-values. We develop techniques to increase the sample size with artificial pseudo p-values, and we assess the impact of those computationally augmented samples of p-values in the power of inferential procedures used to meta-analyse independent tests, namely the routinely used Tippett's and Fisher's methods. On the other hand, using Stouffer's method based on normal scores, we evaluate the number of non-significant results that would be needed to alter a global rejection decision, the most widely used technique of assessing the effect of publication bias. We also present results on characterizations of uniform populations, and we compute closed form expressions to some exact distributions of functions of beta variables, extending our results with uniforms, which are potentially useful for further developments using order statistics and spacings

Combining random number generators

The authors provide some support for the combination generator from a statistical theory viewpoint. The combination generator is generated from taking the fractional part of the sum of several random numbers generators. It is shown that combining several independent generators improves not only the uniformity, but also the independence over each component generator