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Data science is a science that is currently very popular and can be applied in various industries. Of course, the need for proficient people in this field is growing in demand by many businesses, including large corporations. Data science is a science that combines expertise in a particular field of science with programming, mathematics, and statistics skills. The goal is to extract knowledge or information from data. The problem that usually occurs in the data science process is at the data modeling stage, namely the accuracy of the mathematical model that will be used to obtain the estimated parameter values. To overcome this problem, this research was conducted to test the correctness of analytic derivatives in mathematical models and conduct data modeling using analytic derivatives that have been tested to obtain the estimated value of each parameter. The validation process is carried out using an analytic and numeric gradient comparison. If the comparison of the two values is close to zero, then the analytical derivatives used are correct. The parameter estimation method used is the Maximum Likelihood Estimation. In this research, it was concluded that the value of the analytic gradient is the same or close to the numeric gradient value for each parameter so that the analytic derivatives are correct and can be used for the next stage. With the results of this research, the expected implication is to get more accurate data modeling so that the conclusions obtained are more precise. [ABSTRACT FROM AUTHOR]