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Goodness-of-fit procedure for gamma processes

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  • Ghislain Verdier

    (UNIV PAU & PAYS ADOUR / E2S UPPA, IPRA)

Abstract

Gamma processes are commonly used for modelling the accumulative deterioration of systems, in many fields. However, given a series of observations, it is not always easy to affirm that the choice of a gamma process modelling is a good choice. In particular, it would be of great interest to have a statistical test, i.e. a goodness-of-fit test, to answer this question. In this paper, a practical procedure combining three statistical tests is firstly proposed, whose aim is to reject the gamma process modelling as soon as the observations are clearly in contradiction with the basic properties of a homogeneous gamma process, observed with periodic inspections: stationarity, independence and gamma distribution for the increments. The procedure is then extended to non-homogeneous gamma process and aperiodic inspection times. The efficiency of the approach is investigated through numerical simulations, and on real data.

Suggested Citation

  • Ghislain Verdier, 2024. "Goodness-of-fit procedure for gamma processes," Computational Statistics, Springer, vol. 39(5), pages 2623-2650, July.
    • Handle: RePEc:spr:compst:v:39:y:2024:i:5:d:10.1007_s00180-023-01402-z
    DOI: 10.1007/s00180-023-01402-z
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    References listed on IDEAS

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    1. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
    2. Axel Bücher & Jean‐David Fermanian & Ivan Kojadinovic, 2019. "Combining Cumulative Sum Change‐Point Detection Tests for Assessing the Stationarity of Univariate Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 40(1), pages 124-150, January.
    3. Kojadinovic, Ivan & Yan, Jun, 2010. "Modeling Multivariate Distributions with Continuous Margins Using the copula R Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 34(i09).
    4. Massimiliano Giorgio & Agostino Mele & Gianpaolo Pulcini, 2019. "A perturbed gamma degradation process with degradation dependent non‐Gaussian measurement errors," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 35(2), pages 198-210, March.
    5. Christian Genest & Bruno Rémillard, 2004. "Test of independence and randomness based on the empirical copula process," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(2), pages 335-369, December.
    6. Ivan Kojadinovic & Jun Yan, 2011. "Tests of serial independence for continuous multivariate time series based on a Möbius decomposition of the independence empirical copula process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(2), pages 347-373, April.
    7. Pinkse, Joris, 1998. "A consistent nonparametric test for serial independence," Journal of Econometrics, Elsevier, vol. 84(2), pages 205-231, June.
    8. Ghoudi, Kilani & Kulperger, Reg J. & Rémillard, Bruno, 2001. "A Nonparametric Test of Serial Independence for Time Series and Residuals," Journal of Multivariate Analysis, Elsevier, vol. 79(2), pages 191-218, November.
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