Physical Sciences and Mathematics Commons^™

Exact Sampling And Prefix Distributions, Sebastian Oberhoff

Theses and Dissertations

This thesis explores some new means to generate random numbers without incurring any numerical

inaccuracies along the way. In the context of continuous distributions this leads to the discussion of

prex distributions { discrete distributions that fully capture a continuous distribution by describing

their initial digits. These are rst studied graphically, then analytically, which also leads to a general

examination of the behavior of the distribution of trailing digits of continuous distributions. Finally,

some slightly novel, related results from the theory of computation are presented.