Dynamic resource allocation in cloud computing is a critical aspect. It is necessary for computing resources scaling to maintain application performance, reduce costs and ensure the reliability of IT systems. Dynamic resource allocation is possible using open virtual machines (VM), but live migration is a relatively expensive and resource-intensive operation. A number of VM migration algorithms have been proposed, each with different performance characteristics depending on the state of the host system, network, and the VM workload. Recently, a large number of works have emerged that have developed models for assessing the effectiveness of of VM migration, but many of them do not provide a standard of satisfactory prediction accuracy and are built for a single migration algorithm, which limits the use of data models. This work uses a statistical approach to estimate the total migration time and VM downtime based on the approximation of probability densities by Gram-Charlier and Laguerre Series. The proposed method, in comparison with the known ones, allows one to answer the question of what is the probability of total migration time and VM downtime for a given migration type and VM application. The analysis of total migration time and VM downtime is based on the Virtual Machine Live Migration Dataset includes more than 40 000 virtual machine migration records with five different live migration algorithms: post-copy migration, pre-copy migration and its modifications: CPU throttling delta compression, and data compression. The dataset includes approximately 8000 migration records of each migration algorithm with 9 types of workloads. Analysis of the results allows us to conclude that the type of application significantly influences both the shape of the empirical distribution (histograms) of total migration time and its characteristics, therefore it is advisable to obtain an analytical expression for the distribution law of the total migration time and VM downtime taking into account these circumstances. The results of the experiments shows that this method does not depend on the migration algorithm and the type of working application. The use of the Laguerre series can be recommended as giving more reliable results compared to Gram-Charlier series. A method for estimating total migration time and VM downtime can be integrated into a management system to select the best monitoring window for servers and evaluate service-level agreement terms.