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Three parameter gamma-type growth curve, using a stochastic gamma diffusion model: Computational statistical aspects and simulation

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  • Gutiérrez-Sánchez, R.
  • Nafidi, A.
  • Pascual, A.
  • Ramos-Ábalos, E.

Abstract

In this paper, we propose a new model of a three-parameter stochastic growth, based on a stochastic gamma diffusion process, with a third, threshold, parameter. This model can be considered a stochastic version of a three-parameter deterministic growth curve, structured such that its trend function is of the type given by this same growth curve. We develop the statistical inference of this model on the basis of maximum likelihood methodology, analysing on simulated data the computational problem associated with the threshold parameter, a problem that is of great importance in its application to real data.

Suggested Citation

  • Gutiérrez-Sánchez, R. & Nafidi, A. & Pascual, A. & Ramos-Ábalos, E., 2011. "Three parameter gamma-type growth curve, using a stochastic gamma diffusion model: Computational statistical aspects and simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(2), pages 234-243.
    • Handle: RePEc:eee:matcom:v:82:y:2011:i:2:p:234-243
    DOI: 10.1016/j.matcom.2011.06.005
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    References listed on IDEAS

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    1. Tan, W. Y., 1986. "A stochastic Gompertz birth-death process," Statistics & Probability Letters, Elsevier, vol. 4(1), pages 25-28, January.
    2. Gutiérrez, R. & Gutiérrez-Sánchez, R. & Nafidi, A., 2009. "The trend of the total stock of the private car-petrol in Spain: Stochastic modelling using a new gamma diffusion process," Applied Energy, Elsevier, vol. 86(1), pages 18-24, January.
    3. Gutiérrez, R. & Gutiérrez-Sánchez, R. & Nafidi, A., 2006. "Electricity consumption in Morocco: Stochastic Gompertz diffusion analysis with exogenous factors," Applied Energy, Elsevier, vol. 83(10), pages 1139-1151, October.
    4. Gutiérrez, R. & Gutiérrez-Sánchez, R. & Nafidi, A., 2008. "Trend analysis and computational statistical estimation in a stochastic Rayleigh model: Simulation and application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(2), pages 209-217.
    5. Vera, J. Fernando & Di­az-Garci­a, Jose A., 2008. "A global simulated annealing heuristic for the three-parameter lognormal maximum likelihood estimation," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5055-5065, August.
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    Cited by:

    1. Nafidi, A. & Gutiérrez, R. & Gutiérrez-Sánchez, R. & Ramos-Ábalos, E. & El Hachimi, S., 2016. "Modelling and predicting electricity consumption in Spain using the stochastic Gamma diffusion process with exogenous factors," Energy, Elsevier, vol. 113(C), pages 309-318.
    2. Eva María Ramos-Ábalos & Ramón Gutiérrez-Sánchez & Ahmed Nafidi, 2020. "Powers of the Stochastic Gompertz and Lognormal Diffusion Processes, Statistical Inference and Simulation," Mathematics, MDPI, vol. 8(4), pages 1-13, April.

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