A comparison of methods for estimating parameters of the stochastic Lomax process: through simulation study

Abstract

In this paper, we study the problem of parameter estimation of the stochastic Lomax diffusion process, this process was introduced in [A. Nafidi, I. Makroz, and R. Gutiérrez Sánchez, A stochastic lomax diffusion process: Statistical inference and application, Mathematics, 2021][14], and the authors suggested the method of simulated annealing to find the maximum likelihood estimators of this process. In this work, we propose alternative methods for finding the maximum likelihood estimators, namely Genetic algorithm and Nelder-Mead, we also investigate the use of Markov Chain Monte Carlo method to determine the model parameters. Finally, an example of application through the simulation of paths for the process is suggested. Then, a comparison is made between the application of three algorithms based on their accuracy and time of execution.

Keywords

• Lomax diffusion process
• trend analysis
• metaheuristic optimization algorithms
• Markov Chain Monte Carlo
• simulation
• likelihood estimation

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