A Stochastic Lomax Diffusion Process: Statistical Inference and Application

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.

Symmetric and Asymmetric Diffusions through Age-Varying Mixed-Species Stand Parameters

“…The deterministic part in the model is drift function A i (x). Random term D X i (t) B 1 2 • dW i (t), which corresponds to the uncertain part of the model, is referred to as the system noise. In Equation (2),…”

“…Most individual-tree-diameter-growth models were framed using an algebraic difference approach [24] and its mathematical generalizations [25]. The SDE (2) developed in this study enables us to describe a wide range of treeand stand-growth variables. To apply the mixed-effect SDE model defined by Equation (2), we had two adaptation strategies-prediction and forecasting.…”

“…In the past few decades, mathematical models based on diffusion processes were fruitfully applied to describe stochasticity phenomena belonging to even extremely different disciplinary fields that range in scale from human population in biology [2] to cryptocurrency in finance [3] and from infectious disease in medicine [4] to networks in neuroscience [5]. Mixed-effect parameters diffusion processes provide a convenient tool to account for differences between several experiments or several subjects [6].…”

Stochastic Pareto diffusion process : Statistical analysis and computational issues. Simulation and Application

“…Their fields of application range from traditional applications such as economics, physics, and biology, to news technology and the emissions of greenhouse gases. Several SDPs have been developed to model a wide range of problems, such as, Pearson [7]; Weibull [19]; Lomax [17]; Brody [18]; γ-power of the Lundqvist-Korf [6].…”