parameter estimation

In this paper, the probability density function of the process, its trend functions, the maximum likelihood estimate and the confidence interval of the parameters are calculated. This paper investigates a nonhomogeneous state of a diffusion process with a time-dependent velocity reduction coefficient. First, the process probability density function and trend functions are calculated and then, using discrete sampling, statistical inferences such as estimating the parameters by the maximum likelihood method, finding the distribution of the obtained estimators and the confidence interval of the parameters are performed. Finally, for the simulated data, the applications of this model are introduced. In this paper, from the point of view of statistical inference, stochastic differential equation models are studied. A heterogeneous case of a diffusion process with time-dependent deceleration coefficient and stochastic differential equation models with random effects are investigated and an approximation for the nonlinear stochastic differential equation is presented. Also, with the help of time series analysis and statistical methods, the parameters of stochastic differential equation models are estimated.At the end, the application of invariant copulas in the modeling of stochastic differential equations is expressed. In each of these cases, the process probability density function and trend functions are calculated, and statistical inferences such as point estimation, interval estimation, selection of the best model, and numerical analyzes and simulations are performed in stochastic differential equations.

This paper proposed a new method for parameters estimation of the Ornstein Uhlenbeck processes driven with the compound Poisson process. These processes have some applications in modeling and forecasting in financial markets. The proposed estimators are derived based on the method of the moment. In this work, the central limit theorem for the proposed estimators is also established. Numerical experiments are provided to show that the proposed method performs better in comparison with the existing methods, especially in cases when the jumps of the compound Poisson process are relatively rare. As an experimental approach, we fit the Mobarakeh Steel company data with Gamma, Pareto, and Normal Ornstein Uhlenbeck processes and estimate the parameters by using the proposed method. Finally, under these stochastic models, we simulate the volatility of the Mobarakeh Steel Company.

Researchers in different disciplines often face phenomena of random nature. Sometimes it is possible to use probability distributions to describe and predict such phenomena. Each distribution has a number of unknown parameters, whose values are estimated from data. In some problems, there are a few competing distributions for fitting to a data set. In this setup, selecting a suitable model based on some criteria is necessary. This article introduces facilities of R statistical software in performing the above steps. Application of the discussed methods is illustrated using a medical data set.