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Time series models are often used in hydrology to model streamflow series in order to forecast and generate synthetic series which are inputs for the analysis of complex water resources systems. In this paper, we introduce a new modeling approach for hydrologic time series assuming a gamma distribution for the data, where both the mean and conditional variance are being modeled. Bayesian methods using standard Markov Chain Monte Carlo Methods (MCMC) and a simulation algorithm introduced by [1] are used to simulate samples of the joint posterior distribution of interest. An example is given with a time series of monthly averages of natural streamflows, measured from 1931 to 2010 in Furnas hydroelectric dam, in southeastern Brazil. [ABSTRACT FROM AUTHOR]

The generalized exponential distribution, proposed by Gupta and Kundu (1999), is a good alternative to standard lifetime distributions as exponential, Weibull or gamma. Several authors have considered the problem of Bayesian estimation of the parameters of generalized exponential distribution, assuming independent gamma priors and other informative priors. In this paper, we consider a Bayesian analysis of the generalized exponential distribution by assuming the conventional noninformative prior distributions, as Jeffreys and reference prior, to estimate the parameters. These priors are compared with independent gamma priors for both parameters. The comparison is carried out by examining the frequentist coverage probabilities of Bayesian credible intervals. We shown that maximal data information prior implies in an improper posterior distribution for the parameters of a generalized exponential distribution. It is also shown that the choice of a parameter of interest is very important for the reference prior. The different choices lead to different reference priors in this case. Numerical inference is illustrated for the parameters by considering data set of different sizes and using MCMC (Markov Chain Monte Carlo) methods. [ABSTRACT FROM AUTHOR]