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According to the first nth observations of the upper record from exponential distribution, in this article, we can compute maximum likelihood estimation of this distribution parameter. We, then, concentrate on point prediction of the future upper record values in exponential distribution based both on classic and Bayes approaches and second degree and linex loss functions.We, ultimately, deal with numerical comparison available point predictions through Monte Carlo simulation.

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Mathematical methods and statistical distributions present exact results in the climate calculations and hydrological processes. Awareness of the rainfall probability distribution provides the appropriate conditions for water resource planning. Many studies have been done to estimate probability of rainfall by various methods due to the importance of rainfall distribution in the economic, social and particularly agriculture studies. In these studies, the various probabilistic models have been used and the results of the most investigations show that the bivariate gamma distribution branches of gamma model are compatible for rainfall data. The bivariate gamma distribution is used in the hydrological processes modeling. In the present paper, supposing that the X and Y follow the crovelli’s bivariate gamma model, at first a brief description was given in the case of the exact distributions of the functions U=X+Y, P=XY and Q=X⁄((X+Y)) as well as their respective moments, then the validity of this model was evaluated for Rasht airport weather station data. The results showed that rainfall data of this region also confirms The suitability of the crovelli’s bivariate gamma model.

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In this paper, after stating the characteristicof some of continuous distributions including, gamma, Crovelli’s
gamma, Rayleigh, Weibull, Pareto, exponential and generalized gamma distribution with each other,these distributions
were fit on drought data of Guilan state and the best distribution was presented. Then, severity and duration of
the drought of different sites were investigated using standardized precipitation index.

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In analyzing longitudinal data with counted responses, normal distribution is usually used for distribution of the random efffects. However, in some applications random effects may not be normally distributed. Misspecification of this distribution may cause reduction of efficiency of estimators. In this paper, a generalized log-gamma distribution is used for the random effects which includes the normal one as a special case. As the frquentist analysis faces with complex computation, the Bayesian analysis of this model is investigated and then it is utilized for analyzing two real data sets. Also, some simulation studies are conducted to evaluate the performance of the relevant models.