This paper addresses the problem of precisely estimating the parameters of a stochastic model corresponding to branching processes. A branching process is a stochastic process consisting of collections of random variables indexed by the natural numbers. Branching processes are often used to describe population models Jagers (1989) and Athreya and Ney (2012); for example, models in the population genetics showing the genetic drift Burden and Simon (2016) Chen et al. (2017). In contrast to statistical approaches, branching processes enable the study of the dynamics of cell evolution and, as a consistence, have become a popular approach to cancer cell evolution research West et al., 2016. However, particularly in the case of cancer cell evolution, as well as in branching processes in general, the ultimate extinction of a population often occurs Devroye (1998). It is for this reason that with the initial uniform distribution of parameters, branching processes models tend to yield unevenly distributed data consisting of sparse and dense regions. The stochastic nature of the data is an another obstacle in estimating the parameters of a branching processes model, especially in the case of cancer cell evolution Nagornov et al. (2021). Moreover, simulations, based on a model of cell mutations, population evolution, and tumor/cancer subpopulations, commonly lead to the emergence of many clones and rarely to the appearance of cancer cells.