{"title":"A Stochastic Diffusion Process Based on the Two-Parameters Weibull Density Function","authors":"Meriem Bahij, Ahmed Nafidi, Boujem\u00e2a Achchab, S\u00edlvio M. A. Gama, Jos\u00e9 A. O. Matos","country":null,"institution":"","volume":114,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":301,"pagesEnd":307,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10004736","abstract":"Stochastic modeling concerns the use of probability
\r\nto model real-world situations in which uncertainty is present.
\r\nTherefore, the purpose of stochastic modeling is to estimate the
\r\nprobability of outcomes within a forecast, i.e. to be able to predict
\r\nwhat conditions or decisions might happen under different situations.
\r\nIn the present study, we present a model of a stochastic diffusion
\r\nprocess based on the bi-Weibull distribution function (its trend
\r\nis proportional to the bi-Weibull probability density function). In
\r\ngeneral, the Weibull distribution has the ability to assume the
\r\ncharacteristics of many different types of distributions. This has
\r\nmade it very popular among engineers and quality practitioners, who
\r\nhave considered it the most commonly used distribution for studying
\r\nproblems such as modeling reliability data, accelerated life testing,
\r\nand maintainability modeling and analysis. In this work, we start
\r\nby obtaining the probabilistic characteristics of this model, as the
\r\nexplicit expression of the process, its trends, and its distribution by
\r\ntransforming the diffusion process in a Wiener process as shown in
\r\nthe Ricciaardi theorem. Then, we develop the statistical inference of
\r\nthis model using the maximum likelihood methodology. Finally, we
\r\nanalyse with simulated data the computational problems associated
\r\nwith the parameters, an issue of great importance in its application to
\r\nreal data with the use of the convergence analysis methods. Overall,
\r\nthe use of a stochastic model reflects only a pragmatic decision on
\r\nthe part of the modeler. According to the data that is available and
\r\nthe universe of models known to the modeler, this model represents
\r\nthe best currently available description of the phenomenon under
\r\nconsideration.","references":null,"publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 114, 2016"}