The
generalized Pareto-Poisson distribution in THE study of maximum daily total
rainfall

in Piracicaba, SP

Renato Rodrigues SILVA[1]^{}

Silvio
Sandoval ZOCCHI^{1}

§ ABSTRACT: In this study we used the
Generalized Pareto-Poisson distribution to analyze a data set of daily total
rainfall exceeding a threshold value as recorded from 1917 to 2004 in
Piracicaba, SP. The threshold value was chosen so that the excess would follow
a generalized Pareto distribution and the mean cluster size would not differ
from one. Once the threshold value was chosen, the parameters of the model were
estimated using a maximum likelihood method. Based on its estimates, we
estimated the return levels for 10, 25, 500 and 100 years and their 95$\%$
confidence intervals using the likelihood profile method. Moreover, return
periods for daily total rainfall of 40, 60, 80 and 100 mm were calculated. The
goodness of fit of the models were visually evaluated by means of
probability-probability plots and quantile-quantile plots. As a result of the
analysis, a total daily rainfall over 85 mm is expected once every 50 years
from November to March on average, and thus we conclude that, in this period,
the year's highest total daily rainfall is expected.

§ KEYWORDS: Theory value extreme;
return period; level return.

[1] Departamento Ciências Exatas, Universidade de São
Paulo, campus de Piracicaba -- ESALQ/USP, Caixa Postal 9, CEP 13418-900 ,
Piracicaba, SP, Brasil. E-mail: *rrsilva@esalq.usp.br* / *sszocchi@esalq.usp.br*