Research on microbiological groundwater quality was conducted in Chile in a rural watershed that has almost no other water source. Forty-two wells were randomly selected and levels of indicator bacteria -total coliforms (TC), fecal coliforms (FC), and fecal streptococci (FS) -were repeatedly measured during the four seasons of 2005. The aim of this study was to characterize microbiological groundwater quality, relate indicator levels to certain watershed features and management characteristics which are likely to affect water quality. The dynamics of seasonal temporal contamination was determined with statistical analyses of indicator organism concentrations. Nonparametric tests were used to analyze relationships between bacterial indicators in well water and other variables. TC, FC, and FS were found in all samples indicating the wells had been contaminated with human and animal fecal material. The frequency distribution of microorganisms fitted a logistic distribution. The concentrations appeared to be temporal and levels varied between seasons with higher concentrations in winter. The cause of contamination could be linked to the easy access of domestic animals to the wells and to the permeable well casing material. Local precipitation runoff directly influenced the bacterial concentrations found in the wells.
In this paper, we develop a Bartlett correction for the likelihood ratio statistic used to test hypotheses about parameters of a Gaussian stationary and invertible model belonging to the ARMA (autoregressive moving average) family. Alternative hypotheses with and without disturbance parameters are considered. The correction formulae are written in matrix form with the advantage of being easily implemented with the aid of some symbolic or numerical matrix language. Some simulation results are also presented.
In this article we compute three corrected score statistic versions: the Bartlett-type correction and the monotone corrected score statistics proposed by Kakizawa [Biometrika 83 (1996) 923-927] and Cordeiro, Ferrari and Cysneiros [J. Stat. Comput. Simul. 62 (1998) 123-136]. These corrected statistics are used to test the null hypothesis concerning some parameter of interest of an ARMA model, assumed to be Gaussian, stationary and invertible. We also consider the situations where nuisance parameters are present. The formulas are written in matrix form, appropriate for the use of symbolic or numerical languages. Some simulation results are also presented for the AR(1), MA(1) and ARMA(1, 1) models.
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