This paper describes flan, a package providing tools for fluctuation analysis of mutant cell counts. It includes functions dedicated to the distribution of final numbers of mutant cells. Parametric estimation and hypothesis testing are also implemented, enabling inference on different sorts of data with several possible methods. An overview of the subject is proposed. The general form of mutation models is described, including the classical models as particular cases. Estimating from a model, when the data have been generated by another, induces different possible biases, which are identified and discussed. The three estimation methods available in the package are described, and their mean squared errors are compared. Finally, implementation is discussed, and a few examples of usage on real data sets are given.The first estimation method was given by Luria and Delbrück (1943). It is based on the simple relation between the probability of null counts in the sample, and the mutation probability, and it is called P0 method. Of course, if the sample does not contain null counts, the method cannot be applied. Apart from the P0 method, all other methods couple the estimation of π or α, with the estimation of ρ. When the distribution of final numbers has an explicit form, the Maximum Likelihood (ML) is an obvious optimal choice (Ma et al., 1992;Zheng, 2005). However, because of the jackpots, likelihood computation can be numerically unstable. There are several ways to reduce tail effects (Wilcox, 2012, Sec. 2.2), among which "Winsorization" consists in truncating the sample beyond some maximal value. Another estimation method (GF) uses the probability generating function (PGF) (Rémillard and Theodorescu, 2000;Hamon and Ycart, 2012). The estimators of α and ρ obtained with the GF method proved to be close to optimal efficiency, with a broad range of calculability, a good numerical stability, and a negligible computing time. For the three methods, P0, ML, and GF, the estimators of α and
