**Commenced**in January 2007

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**Edition:**International

**Paper Count:**30127

##### A Stochastic Diffusion Process Based on the Two-Parameters Weibull Density Function

**Authors:**
Meriem Bahij,
Ahmed Nafidi,
Boujemâa Achchab,
Sílvio M. A. Gama,
José A. O. Matos

**Abstract:**

**Keywords:**
Diffusion process,
discrete sampling,
likelihood
estimation method,
simulation,
stochastic diffusion equation,
trends
functions,
bi-parameters Weibull density function.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1125047

**References:**

[1] R. F. Woolson and W. R. Clarke, Statistical Methods for the Analysis of Biomedical Data, 2nd ed. John Wiley & Sons, Vol.371, New York, United States, 2000.

[2] R. L. Mason, R. F. Gunst, and J. L. Hess Statistical Design and Analysis of Experiments: with Applications to Engineering and Science,Wiley, New York, United States, 1989.

[3] W. R. Blischke and D. N. P. Murthy, Probability distributions for modeling time to failure, in Reliability: Modeling, Prediction, and Optimization, John Wiley & Sons, Inc.,Hoboken, NJ, USA, 2000.

[4] S. A. Klugman, and R. Parsa, Fitting bivariate loss distributions with copulas, Insurance: Mathematics and Economics, Elsevier, Vol. 24, no.1, 1999, pp. 139–148.

[5] D. J. Davis, An Analysis of some Failure Data, Journal of the American Statistical Association, Taylor & Francis Group, Vol. 47, no.250, 1952, pp. 113–150.

[6] P. Feigl and M. Zelen, Estimation of exponential survival probabilities with concomitant information, Biometrics, JSTOR, 1965, pp. 826–838.

[7] D. R Cox, Renewal Theory Methuen, CoxRenewal Theory1962, London, 1962.

[8] E. J. Gumbel, Statistics of extremes. 1958, Columbia Univ. press, New York, 1958.

[9] J. Lieblein and M. Zelen, Statistical investigation of the fatigue life of deep-groove ball bearings, Journal of Research of the National Bureau of Standards, Citeseer, Vol. 57, no.5, 1956, pp. 273–316.

[10] M. C. Pike, A method of analysis of a certain class of experiments in carcinogenesis, Biometrics, JSTOR, Vol. 22, no.1, 1966, pp. 142–161.

[11] J. W. Boag, Maximum Likelihood Estimates of the Proportion of Patients Cured by Cancer Therapy, Journal of the Royal Statistical Society. Series B (Methodological), Royal Statistical Society, Wiley, Vol. 11, no.1, 1949, pp. 15–53.

[12] A. N. Giovanis and C. H. Skiadas, A Stochastic Logistic Innovation Diffusion Model Studying the Electricity Consumption in Greece and the United States, Technological Forecasting and Social Change, Vol. 61, 1999, pp. 235–246.

[13] A. Katsamaki and C. H. Skiadas, Analytic solution and estimation of parameters on stochastics exponential model for a technological diffusion process, Applied Stochastics Model and Data Analysis, Vol. 11, 1995, pp. 59–75.

[14] C. Skiadas and A. Giovani, A stochastic bass innovation diffusion model for studying the growth of electricity consumption in Greece, Applied Stochastic Models and Data Analysis, Vol. 13, 1997, pp. 85–101.

[15] R. Gutie´rrez-Sa´nchez, A. Nafidi, A. Pascual, E. R. A´ balos, Three parameter gamma-type growth curve, using a stochastic gamma diffusion model: Computational statistical aspects and simulation, Mathematics and Computers in Simulation, Vol. 82, 2011, pp. 234–243.

[16] R. Guti´errez, R. Guti´errez-S´anchez, A. Nafidi and E. Ramos, A diffusion model with cubic drift: statistical and computational aspects and application to modeling of the global CO2 emission in Spain, Environmetrics, Vol. 18, 2007, pp. 55–69.

[17] R. Guti´errez, R. Guti´errez-S´anchez, A. Nafidi and E. Ramos, Studying the vehicule park in Spain using the lognormal and Gompertz diffusion processes, Proceedings od SEIO’04, Vol. 18, 2004, pp. 171–172.

[18] A. V. Egorov, H. Li, and Y. Xu, Maximum likelihood estimation of time-inhomogeneous diffusions, Journal of Econometric, Vol. 114, 2003, pp. 107–139.

[19] Y. Ait-Sahalia, R. Kimmel, Maximum likelihood estimation of stochastic volatility models, Journal of Financial Economics, Vol. 83, 2007, pp. 413–452.

[20] F. Casas, Solution of linear partial differential equations by Lie algebraic methods, Journal of Computational and Applied Mathematics, Vol. 76, 1996, pp. 159–170.

[21] P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Springer-Verlag, Applications of Mathematics Series, no.23, 1991.

[22] LM. Ricciardi, Diffusion processes and related topics in biology. Lecture notes in biomathematics, Springer-Verlag, Berlin, 1977.

[23] P. W. Zenha, Invariance of Maximum Likelihood Estimators, The Annals of Mathematical Statistics, Ann. Math. Statist., Vol. 37, no.3, 1966, pp. 744.