A Stochastic Lomax Diffusion Process: Statistical Inference and Application

Ahmed Nafidi, Ilyasse Makroz and Ramón Gutiérrez Sánchez
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Ahmed Nafidi: Department of Mathematics and Informatics, National School of Applied Sciences, Hassan First University of Settat, LAMSAD, Avenue de l’université, Berrechid BP 280, Morocco
Ilyasse Makroz: Department of Mathematics and Informatics, National School of Applied Sciences, Hassan First University of Settat, LAMSAD, Avenue de l’université, Berrechid BP 280, Morocco
Ramón Gutiérrez Sánchez: Department of Statistics and Operational Research, Facultad de Ciencias, Campus de Fuentenueva, University of Granada, 18071 Granada, Spain

Mathematics, 2021, vol. 9, issue 1, 1-9

Abstract: 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.

Keywords: stochastic differential equation; lomax distribution; trend functions; statistical inference; simulated annealing; adolescent fertility rate (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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