This article addresses the various properties and different methods of estimation of the unknown parameters of Gompertz distribution. Although, our main focus is on estimation from both frequentist and Bayesian point of view, yet, various mathematical and statistical properties of the Gompertz distribution (such as quantiles, moments, moment generating function, hazard rate, mean residual lifetime, mean past lifetime, stochasic ordering, stressstrength parameter, various entropies, Bonferroni and Lorenz curves and order statistics) are derived. We briefly describe different frequentist approaches, namely, maximum likelihood estimators, moments estimators, pseudo-moments estimators, modified moments estimators, L-moment estimators, percentile based estimators, least squares and weighted least squares estimators, maximum product of spacings estimators, minimum spacing

RESUMOConsiderando a importância sócio-econômica da região de Presidente Prudente, este estudo teve como objetivo estimar a precipitação pluvial máxima esperada para diferentes níveis de probabilidade e verificar o grau de ajuste dos dados ao modelo Gumbel, com as estimativas dos parâmetros obtidas pelo método de máxima verossimilhança. Pelos resultados, o teste de Kolmogorov-Sminorv (K-S) mostrou que a distribuição Gumbel testada se ajustou com p-valor maior que 0.28 para todos os períodos de tempo considerados, comprovando que a distribuição Gumbel apresenta um bom ajustamento aos dados observados para representar as precipitações pluviais máximas. As estimativas de precipitação obtidas pelo método de máxima verossimilhança são consistentes, conseguindo reproduzir com bastante fidelidade o regime de chuvas da região de Presidente Prudente. Assim, o conhecimento da distribuição da precipitação pluvial máxima mensal e das estimativas das precipitações diárias máximas esperadas, possibilita um planejamento estratégico melhor, minimizando assim o risco de ocorrência de perdas econômicas para essa região. Palavras-Chave: Precipitação máxima, estimador de máxima verossimilhança, distribuição Gumbel, intervalo de confiança. ABSTRACT: STUDY OF THE MAXIMUM ANNUAL PRECIPITATION IN PRESIDENTE PRUDENTEConsidering the socioeconomic importance of Presidente Prudente area, this study aimed at to estimate the maximum pluvial precipitation expected for different levels of probability and to check the fitting degree of the data to the Gumbel model, with the parameter estimation obtained by the maximum likelihood approach. The Kolmogorov-Sminorv (K-S) test showed that the Gumbel distribution has fitted with p-value larger than 0.28 for all of the time periods considered, showing that the Gumbel distribution presents a good fitting to the observed data representing the maximum pluvial precipitations values. The precipitation estimates obtained by the maximum likelihood approach are consistent allowing to reproduce with plenty reliability the rainfall regime for Presidente Prudente region. Therefore, the knowledge of the monthly maximum pluvial precipitation distribution and the expected maximum daily precipitation estimates permits a better strategic planning thus minimizing the risk of economical losses for this region.

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The Generalized gamma (GG) distribution plays an important role in statistical analysis. For this distribution, we derive non-informative priors using formal rules, such as Jeffreys prior, maximal data information prior and reference priors. We have shown that these most popular formal rules with natural ordering of parameters, lead to priors with improper posteriors. This problem is overcome by considering a prior averaging approach discussed in Berger et al. [Overall objective priors. Bayesian Analysis. 2015;10(1):189-221]. The obtained hybrid Jeffreys-reference prior is invariant under one-to-one transformations and yields a proper posterior distribution. We obtained good frequentist properties of the proposed prior using a detailed simulation study. Finally, an analysis of the maximum annual discharge of the river Rhine at Lobith is presented.

In this paper, we introduce a Bayesian analysis for a bivariate generalized exponential distribution in the presence of censored data and covariates derived from Copula functions. The generalized exponential distribution could be a good alternative to analyze lifetime data in comparison to usual existing parametric lifetime distributions as Weibull or Gamma distributions. We have being using standard existing MCMC (Markov Chain Monte Carlo) methods to simulate samples for the joint posterior of interest. Two examples are introduced to illustrate the proposed methodology: an example with simulated bivariate lifetime data and an example with a real lifetime data set.

This paper takes into account the estimation for the unknown parameters of the Gompertz distribution from the frequentist and Bayesian view points by using both objective and subjective prior distributions. We first derive non-informative priors using formal rules, such as Jefreys prior and maximal data information prior (MDIP), based on Fisher information and entropy, respectively. We also propose a prior distribution that incorporate the expert's knowledge about the issue under study. In this regard, we assume two independent gamma distributions for the parameters of the Gompertz distribution and it is employed for an elicitation process based on the predictive prior distribution by using Laplace approximation for integrals. We suppose that an expert can summarize his/her knowledge about the reliability of an item through statements of percentiles. We also present a set of priors proposed by Singpurwala assuming a truncated normal prior distribution for the median of distribution and a gamma prior for the scale parameter. Next, we investigate the effects of these priors in the posterior estimates of the parameters of the Gompertz distribution. The Bayes estimates are computed using Markov Chain Monte Carlo (MCMC) algorithm. An extensive numerical simulation is carried out to evaluate the performance of the maximum likelihood estimates and Bayes estimates based on bias, mean-squared error and coverage probabilities. Finally, a real data set have been analyzed for illustrative purposes.

This study was undertaken to investigate the opinion of nursing undergraduate students of the first year about the discipline "Informatic applied to health". Data were collected using a questionnaire with open and closed questions applied through three consecutive years (1989, 1990, 1991). The results showed that undergraduate students considered this course important. Student's expectations were related to the necessity to get familiar with computers. The mentioned critiques were related to the necessity of more time and equipments to support a better learning process.

A Bayesian analysis was developed with different noninformative prior distributions such as Jeffreys, Maximal Data Information, and Reference. The aim was to investigate the effects of each prior distribution on the posterior estimates of the parameters of the extended exponential geometric distribution, based on simulated data and a real application.