Analytic solution and estimation of parameters on a stochastic exponential model for a technological diffusion process

Katsamaki, Anastasia; Skiadas, Christos H.

doi:10.1002/asm.3150110108

Cited by 25 publications

(11 citation statements)

References 11 publications

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“…4. It is possible to construct a confidence region of the trajectories of the Gompertz process, based on the explicit expression of its random variables X (t) and following a known methodology (see, for example, Katsamaki and Skiadas [39]). In particular, for the fitted Gompertz process (with the technical parameters replaced by their estimators), the following lines can be calculated for a confidence of (1− )%.…”

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confidence: 99%

Modelling and forecasting vehicle stocks using the trends of stochastic Gompertz diffusion models: The case of Spain

Gutiérrez

Gutiérrez-Sánchez

Nafidi

2008

Appl Stoch Models Bus & Ind

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In the present study, we treat the stochastic homogeneous Gompertz diffusion process (SHGDP) by the approach of the Kolmogorov equation. Firstly, using a transformation in diffusion processes, we show that the probability transition density function of this process has a lognormal time-dependent distribution, from which the trend and conditional trend functions and the stationary distribution are obtained. Second, the maximum likelihood approach is adapted to the problem of parameters estimation in the drift and the diffusion coefficient using discrete sampling of the process, then the approximated asymptotic confidence intervals of the parameter are obtained. Later, we obtain the corresponding inference of the stochastic homogeneous lognormal diffusion process as limit from the inference of SHGDP when the deceleration factor tends to zero. A statistical methodology, based on the above results, is proposed for trend analysis. Such a methodology is applied to modelling and forecasting vehicle stocks. Finally, an application is given to illustrate the methodology presented using real data, concretely the total vehicle stocks in Spain.

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confidence: 99%

Modelling and forecasting vehicle stocks using the trends of stochastic Gompertz diffusion models: The case of Spain

Gutiérrez

Gutiérrez-Sánchez

Nafidi

2008

Appl Stoch Models Bus & Ind

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“…-Moreover, the trend function of the process, given in Equation (9), is corresponding to the PDF of the Weibull distribution.…”

Section: Moments Of the Processmentioning

confidence: 99%

Two-Parameter Stochastic Weibull Diffusion Model: Statistical Inference and Application to Real Modeling Example

et al. 2020

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This paper describes the use of the non-homogeneous stochastic Weibull diffusion process, based on the two-parameter Weibull density function (the trend of which is proportional to the two-parameter Weibull probability density function). The trend function (conditioned and non-conditioned) is analyzed to obtain fits and forecasts for a real data set, taking into account the mean value of the process, the maximum likelihood estimators of the parameters of the model and the computational problems that may arise. To carry out the task, we employ the simulated annealing method for finding the estimators values and achieve the study. Finally, to evaluate the capacity of the model, the study is applied to real modeling data where we discuss the accuracy according to error measures.

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“…Owing, to the existence of these disturbances, some authors have proposed models which relax the deterministic nature of the parameters in aggregate diffusion models assuming for example that some parameters follow a simple random walk process (Lilien et al, 1981;Eliashberg et al, 1987). Another approach to the problem of introducing stochasticity into the model is the use of Ito's stochastic differential equations by considering an infinitesimal variance in the adoption pattern between two successive states of the growth process (Skiadas et al, 1993;1994;Giovanis, 1995;Katsamaki and Skiadas, 1995) in order to take into account the internal and/or external fluctuations.…”

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A stochastic Bass innovation diffusion model for studying the growth of electricity consumption in Greece

Skiadas

Giovanis

1997

Appl. Stochastic Models Data Anal.

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In this paper a stochastic innovation diffusion model is proposed derived by introducing stochasticity into the well‐known Bass model. The stochastic model is solved analytically by using the theory of reducible stochastic differential equations and the first moment of the resulting stochastic process is presented. The parameter estimators of the model are derived by using a procedure which provides the maximum likelihood estimators (MLE) using time series data. Finally, the model is applied to the data of electricity consumption in Greece. Using a simulation technique, it is possible to predict the performance of the consumption process by defining a subdomain to which all possible trajectories of the process should belong with a predefined probability. © 1997 by John Wiley & Sons, Ltd.

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Analytic solution and estimation of parameters on a stochastic exponential model for a technological diffusion process

Cited by 25 publications

References 11 publications

Modelling and forecasting vehicle stocks using the trends of stochastic Gompertz diffusion models: The case of Spain

Modelling and forecasting vehicle stocks using the trends of stochastic Gompertz diffusion models: The case of Spain

Two-Parameter Stochastic Weibull Diffusion Model: Statistical Inference and Application to Real Modeling Example

A stochastic Bass innovation diffusion model for studying the growth of electricity consumption in Greece

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