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Weibull and generalised exponential overdispersion models with an application to ozone air pollution

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  • Jorge Alberto Achcar
  • Edilberto Cepeda-Cuervo
  • Eliane R. Rodrigues

Abstract

We consider the problem of estimating the mean and variance of the time between occurrences of an event of interest (inter-occurrences times) where some forms of dependence between two consecutive time intervals are allowed. Two basic density functions are taken into account. They are the Weibull and the generalised exponential density functions. In order to capture the dependence between two consecutive inter-occurrences times, we assume that either the shape and/or the scale parameters of the two density functions are given by auto-regressive models. The expressions for the mean and variance of the inter-occurrences times are presented. The models are applied to the ozone data from two regions of Mexico City. The estimation of the parameters is performed using a Bayesian point of view via Markov chain Monte Carlo (MCMC) methods.

Suggested Citation

  • Jorge Alberto Achcar & Edilberto Cepeda-Cuervo & Eliane R. Rodrigues, 2012. "Weibull and generalised exponential overdispersion models with an application to ozone air pollution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(9), pages 1953-1963, May.
    • Handle: RePEc:taf:japsta:v:39:y:2012:i:9:p:1953-1963
    DOI: 10.1080/02664763.2012.697132
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    1. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    2. J. Polzehl & V. G. Spokoiny, 2000. "Adaptive weights smoothing with applications to image restoration," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 335-354.
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    1. M. Alizadeh & S. Rezaei & S. Bagheri & S. Nadarajah, 2015. "Efficient estimation for the generalized exponential distribution," Statistical Papers, Springer, vol. 56(4), pages 1015-1031, November.

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