RESUMO Neste trabalho, apresentamos diferentes métodos de estimação para os parâmetros da distribuição binomial-exponencial 2, tais como, estimador de máxima verossimilhança, método dos momentos, método percentil, estimador de mínimos quadrados, método do máximo produto espaçado, estimador de Cramér-von-Mises, estimador de Anderson-Darling e o estimador de Anderson-Darling com cauda a direita são apresentados. Com base em um estudo de simulação numérica, verificamos que o estimador de Anderson-Darling retorna estimativas mais eficientes se comparado com os outros estimadores. Por fim, nossa proposta é aplicada em três conjuntos de dados relacionados à pluviosidade total mensal ao longo dos meses de Abril, Maio e Setembro em São Carlos, Brasil.

ABSTRACT In this paper, we have considered different estimation methods of the unknown parameters of a binomial-exponential 2 distribution. First, we briefly describe different methods of estimation such as maximum likelihood, method of moments, percentile based estimation, least squares, method of maximum product of spacings, method of Cramér-von-Mises, methods of Anderson-Darling and right-tail Anderson-Darling, and compare them using extensive simulations studies. Finally, the potentiality of the model is studied using three real data sets related to the total monthly rainfall during April, May and September at São Carlos, Brazil.

We report here the construction of a vector derived from pET3-His and pRSET plasmids for the expression and purification of recombinant proteins in Escherichia coli based on T7 phage RNA polymerase. The resulting pAE plasmid combined the advantages of both vectors: small size (pRSET), expression of a short 6XHis tag at N-terminus (pET3-His) and a high copy number of plasmid (pRSET). The small size of the vector (2.8 kb) and the high copy number/cell (200-250 copies) facilitate the subcloning and sequencing procedures when compared to the pET system (pET3-His, 4.6 kb and 40-50 copies) and also result in high level expression of recombinant proteins (20 mg purified protein/liter of culture). In addition, the vector pAE enables the expression of a fusion protein with a minimal amino-terminal hexa-histidine affinity tag (a tag of 9 amino acids using XhoI restriction enzyme for the 5'cloning site) as in the case of pET3-His plasmid and in contrast to proteins expressed by pRSET plasmids (a tag of 36 amino acids using BamHI restriction enzyme for the 5'cloning site). Thus, although proteins expressed by pRSET plasmids also have a hexa-histidine tag, the fusion peptide is much longer and may represent a problem for some recombinant proteins.