1 Operations Research, Department of Informatics and Mathematical Modeling, Technical University of Denmark2 Department of Informatics and Mathematical Modeling, Technical University of Denmark3 Department of Transport, Technical University of Denmark
Random numbers are used for a great variety of applications in almost any field of computer and economic sciences today. Examples ranges from stock market forecasting in economics, through stochastic traffic modelling in operations research to photon and ray tracing in graphics. The construction of a model or a solution method requires certain characteristics of the random numbers used. This is usually a distribution classification, which the sequence of random numbers must fulfill; of these some are very hard to fulfill and others are next to impossible. Today mathematics allows us to transform distributions into others with most of the required characteristics. In essence, a uniform sequence which is transformed into a new sequence with the required distribution. The subject of this article is to consider the well known highly uniform Halton sequence and modifications to it. The intent is to generate highly uniform multidimensional draws, which are highly relevant for todays traffic models. This paper shows among others combined shuffling and scrambling seems needless, that scrambling gives the lowest correlation and that there are detectable differences between random numbers, dependent on their generation.
Shuffled Halton; a priori distribution; random numbers; Halton numbers; Mixed Logit estimation; Leaped Halton.; Scrambled Halton