scholarly journals Two Stochastic Differential Equations for Modeling Oscillabolastic-Type Behavior

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 155
Author(s):  
Antonio Barrera ◽  
Patricia Román-Román ◽  
Francisco Torres-Ruiz
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Maximum Likelihood ◽  
Numerical Methods ◽  
Stochastic Models ◽  
Maximum Likelihood Method ◽  
Diffusion Processes ◽  
Oscillatory Behavior ◽  
Likelihood Method ◽  
Systems Of Equations

Stochastic models based on deterministic ones play an important role in the description of growth phenomena. In particular, models showing oscillatory behavior are suitable for modeling phenomena in several application areas, among which the field of biomedicine stands out. The oscillabolastic growth curve is an example of such oscillatory models. In this work, two stochastic models based on diffusion processes related to the oscillabolastic curve are proposed. Each of them is the solution of a stochastic differential equation obtained by modifying, in a different way, the original ordinary differential equation giving rise to the curve. After obtaining the distributions of the processes, the problem of estimating the parameters is analyzed by means of the maximum likelihood method. Due to the parametric structure of the processes, the resulting systems of equations are quite complex and require numerical methods for their resolution. The problem of obtaining initial solutions is addressed and a strategy is established for this purpose. Finally, a simulation study is carried out.

scholarly journals Data bank: nine numerical methods for determining the parameters of weibull for wind energy generation tested by five statistical tools

2021 ◽  
Vol 12 (2) ◽  
pp. 1114
Author(s):  
Ahmed Samir Badawi ◽  
Siti Hajar Yusoff ◽  
Alhareth Mohammed Zyoud ◽  
Sheroz Khan ◽  
Aisha Hashim ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Numerical Methods ◽  
Root Mean Square Error ◽  
Mean Square Error ◽  
Root Mean Square ◽  
Prediction Accuracy ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Mean Square ◽  
Modified Maximum Likelihood

This study aims to determine the potential of wind energy in the mediterranean coastal plain of Palestine. The parameters of the Weibull distribution were calculated on basis of wind speed data. Accordingly, two approaches were employed: analysis of a set of actual time series data and theoretical Weibull probability function. In this analysis, the parameters Weibull shape factor ‘<em>k</em>’ and the Weibull scale factor ‘<em>c</em>’ were adopted. These suitability values were calculated using the following popular methods: method of moments (MM), standard deviation method (STDM), empirical method (EM), maximum likelihood method (MLM), modified maximum likelihood method (MMLM), second modified maximum likelihood method (SMMLM), graphical method (GM), least mean square method (LSM) and energy pattern factor method (EPF). The performance of these numerical methods was tested by root mean square error (RMSE), index of agreement (IA), Chi-square test (X<sup>2</sup>), mean absolute percentage error (MAPE) and relative root mean square error (RRMSE) to estimate the percentage of error. Among the prediction techniques. The EPF exhibited the greatest accuracy performance followed by MM and MLM, whereas the SMMLM exhibited the worst performance. The RMSE achieved the best prediction accuracy, whereas the RRMSE attained the worst prediction accuracy.

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