A Stochastic Lomax Diffusion Process: Statistical Inference and Application Nafidi, Ahmed Makroz, Ilyasse Gutiérrez Sánchez, Ramón Stochastic differential equation Lomax distribution Trend function Statistical inference Simulated annealing Adolescent fertility rate The authors are very grateful to Editor and referees for consecutive comments and suggestions. This research has been funded by "FEDER/Junta de Andalucia-Consejeria de Economia y Conocimiento/ Proyecto A-FQM-228-UGR18". In this paper, we discuss a new stochastic diffusion process in which the trend function is proportional to the Lomax density function. This distribution arises naturally in the studies of the frequency of extremely rare events. We first consider the probabilistic characteristics of the proposed model, including its analytic expression as the unique solution to a stochastic differential equation, the transition probability density function together with the conditional and unconditional trend functions. Then, we present a method to address the problem of parameter estimation using maximum likelihood with discrete sampling. This estimation requires the solution of a non-linear equation, which is achieved via the simulated annealing method. Finally, we apply the proposed model to a real-world example concerning adolescent fertility rate in Morocco. 2021-03-03T08:29:16Z 2021-03-03T08:29:16Z 2021-01-05 info:eu-repo/semantics/article Nafidi, A.; Makroz, I.; Gutiérrez-Sánchez, R. A Stochastic Lomax Diffusion Process: Statistical Inference and Application. Mathematics 2021, 9, 100. [https://doi. org/10.3390/math9010100] http://hdl.handle.net/10481/66796 10.3390/math9010100 eng http://creativecommons.org/licenses/by/3.0/es/ info:eu-repo/semantics/openAccess Atribución 3.0 España MDPI