Estimation of Mutation Rates from Fluctuation Experiments via Probability Generating Functions

This paper calculates probability distributions modeling the Luria-Delbr\"uck experiment. We show that by thinking purely in terms of generating functions, and using a 'backwards in time' paradigm, that formulas describing various situations can be easily obtained. This includes a generating function for Haldane's probability distribution due to Ycart. We apply our formulas to both simulated and real data created by looking at yeast cells acquiring an immunization to the antibiotic canavanine. This paper is somewhat incomplete, having been last significantly modified in March 29, 2014. However the first author feels that this paper has some worthwhile ideas, and so is going to make this paper publicly available.