# Continuous Lattices Proc. conf. Bremen, 1979 by B. Banaschewski, R.-E. Hoffmann By B. Banaschewski, R.-E. Hoffmann

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We had 14, 10, 12, 6, and 9 exceedances during spring for regions NE, NW, CE, SE, and SW, respectively, and there were 5, 7, 4, 5, and 5 exceedances during winter. 17 ppm was not surpassed in any of the seasons. Autumn is the season with no exceedances of the threshold in regions NE, NW, and SW. However, there were 2 and 3 exceedances during autumn in regions CE and SE, respectively. There were no exceedances during summer in region NE and there were 2, 1, 6, and 4 exceedances in regions CE, NW, SW, and SE, respectively.

9) 32 3 Poisson Models and Their Application to Ozone Data where v1 and v2 are as in Model I. 9) is that the terms φ a −1 and e−b φ do not appear. When Model III is considered, the parameter θ I will have the same prior distribution as the one considered in Model I, with possibly different values for its hyperparameters. The random quantity σw2 is assumed to have a Gamma(a , b ) prior distribution. 10) j=1 where v1 and v2 are as in Models I and II. Posterior summaries of interest are obtained from simulated samples from the joint posterior distribution using the MCMC algorithm internally implemented in the software WinBugs.

Since a non-homogenous Poisson model is assumed, for D = {d1 , d2 , . . 13) i=1 where λ (t | θ ) and m(t | θ ) are the rate and mean functions, respectively, of the Poisson process N . Remark. In  and , the expression for the likelihood function has the factor exp[−m(dK | θ )] instead of exp[−m(T | θ )]. This is so because the observation stopped at the Kth surpassing (see ). In order to illustrate the use of non-homogeneous Poisson process, take for instance the case of the exponentiated-Weibull rate function considered in .