Finding the probability distribution of the random survival variable is an important task both in that theory and in reliability. To find its distribution, a procedure based on characteristic vectors is proposed. Firstly, from the sample observations, the sample characteristic vector VCM is constructed, whose elements are the sample percentiles 05, 10, 16, 25, 50, 75, 84, 90 and 95. On the other hand, a selection of probability distributions is made that have the highest likelihood. In each of the selected ones, the necessary calculations are made to estimate these percentiles and thus form the characteristic vectors of each distribution: VCDi. The probability distribution whose characteristic vector is closest to the sample characteristic vector is the distribution selected to explain the behavior of the survival random variable. To exemplify the method, data from the project are used: Mathematical modeling, numerical experimentation and computational simulation of the differentiation, maintenance and self-renewal phenomenon of clinical hematopoietic stem cells.