Luria-Delbrück fluctuation analysis: estimating the Poisson parameter in a compound Poisson distribution.

Estimating the mutation rate from a Luria-Delbrück fluctuation experiment involves estimating the Poisson parameter in a compound Poisson distribution. The efficiency with which this can be estimated depends on how well the other random factors have been characterized. The assumption that cell growth can be represented as a stochastic pure birth or Yule process is biologically unrealistic but contributes little to the bias and variance of a maximum likelihood estimator of the mutation rate.