Modifications and Alternatives to the Tests of Levene and Brown & Forsythe for Equality of Variances and Means

The usual tests to compare variances and means (e. g. Bartlett`s test and F-test) assume that the sample comes from a normal distribution. In addition, the test for equality of means requires the assumption of homogeneity of variances. In some situation those assumptions are not satisfied, hence we may face problems like excessive size and low power. In this paper, we describe two tests, namely the Levene`s test for equality of variances, which is robust under nonnormality; and the Brown and Forsythe`s test for equality of means. We also present some modifications of the Levene`s test and Brown and Forsythe`s test, proposed by different authors. We analyzed and applied one modified form of Brown and Forsythe`s test to a real data set. This test is a robust alternative under nonnormality, heteroscedasticity and also when the data set has influential observations. The equality of variance can be well tested by Levene`s test with centering at the sample median.

Dynamics of Dissolved Forms of Carbon and Inorganic Nitrogen in Small Watersheds of the Coastal Atlantic Forest in Southeast Brazil

Based on the fact that streamwater quality reflects landscape conditions, the objectives of this study were: to investigate nitrogen (N), carbon (C), and major ion concentrations in six streams crossing minimally disturbed Atlantic Forest areas, with similar geomorphological characteristics; to determine N and C fluxes in one of these pristine streams (Indaia); and assess the impact of human activity on the biogeochemistry of two other streams in the same region, crossing urbanized areas. The distribution pattern of carbon and inorganic nitrogen dissolved forms, as well as the major ion and biogenic gas concentrations in the streamwater, was similar in pristine streams, indicating that the C and N dynamics were determined by influence of some factors, such as climate, atmospheric deposition, geology, soil type, and land covering, which were analogous in the forested watersheds. The urban streams were significantly different from the pristine streams, showing low dissolved oxygen concentrations, high respiration rates, and high concentrations of carbon dioxide, dissolved inorganic nitrogen, dissolved inorganic carbon, and major ion. These differences were attributed to anthropogenic impact on water quality, especially domestic sewage discharge. Additionally, in the Indaia stream, it was possible to observe the importance of rainfall over temporal dynamics of dissolved carbon forms, and also, the obtained specific flux of dissolved inorganic nitrogen was relatively elevated (approximately 11 kg ha(-1) year(-1)). These results reveal the influence of human activity over the biogeochemistry of coastal streams and also indicate the importance N export of Atlantic Forest to the ocean.

Boron isotope composition of tourmalinite and vein tourmalines associated with gold mineralization, Serra do Itaberaba Group, central Ribeira Belt, SE Brazil

Important concentrations of tourmaline occur as gold-bearing stratiform tourmalinites and in mineralized quartz-tourmaline veins at the Tapera Grande and Quartzito gold prospects in the Mesoproterozoic Serra do Itaberaba Group, central Ribeira Belt (Sao Paulo State, SE Brazil). The main rock types in both prospects constitute the volcanic-sedimentary Morro da Pedra Preta Formation, which formed in a submarine back-arc setting. At Tapera Grande, the volcanic-sedimentary sequence is composed of metabasic and metavolcaniclastic rocks, graphitic and sulfur-rich metapelites, banded iron formation, metandesite, metarhyolite, calcsilicates, tourmalinites and metahydrothermalites derived from mafic and felsic rocks. The Mesoproterozoic rocks at Quartzito prospect are lithologically similar but they have been affected by Neoproterozoic faulting and shearing and by the emplacement of granitic rocks, resulting in the formation of tourmaline-rich quartz-carbonate veins with gold and base metal mineralization. We conducted a chemical and B-isotope study of tourmalines in order to better understand the origin of the stratiform tourmalinites in the Morro da Pedra Preta Formation and their relationship with gold mineralization. The overall range of delta(11)B values obtained for the tourmalinite and vein tourmalines is between - 15%. and -5 parts per thousand, with the tourmalinites failing at the low end of this range (-15 to -8 parts per thousand). Such values are typical for continental crust and inconsistent with a primary marine boron signature as expected from the submarine-exhalative model for the gold prospects. We conclude from this that tourmaline formed or recrystallized from crustal fluids related to the amphibolite-grade metamorphism which affected the Serra do Itaberaba Group and that gold deposition occurred syn- to post-peak metamorphism by phase immiscibility, as attested by fluid inclusions in Tapera Grande tourmalinite tourmaline and quartz. The vein-hosted tourmalines at Quartzito have isotopically variable boron signatures, with heavier delta(11)B values of -5 parts per thousand to -8 parts per thousand for acicular green tourmalines and lighter values (-15 parts per thousand to -7 parts per thousand for light blue, Ti-firee tourmaline from quartz-carbonate veins). We attribute the heavier boron to fluids derived from the volcano-sedimentary rocks of marine affinity whereas the lighter boron was contributed by crustal fluids related to the granitoids or metasediments in the continental crust. (c) 2009 Elsevier B.V. All rights reserved.

Fabrics of pre- and syntectonic granite plutons and chronology of shear zones in the Eastern Borborema Province, NE Brazil

We used the fabrics of two granite plutons and U/Pb (SHRIMP) zircon ages to constrain the tectonic evolution of the E-trending Patos shear zone (Borborema Province, NE Brazil). The pre-tectonic Teixeira batholith consists of an amphibole leucogranite locally with aegirine-augite. Zircons from a syenogranite yielded crystallization ages of 591 +/- 5 Ma. The batholith fabrics were determined by anisotropy of magnetic susceptibility (AMS) and mineral shape preferred orientation. The fabrics support pre-transcurrent batholith emplacement, as evidenced by: (i) magmatic/magnetic fabrics in low susceptibility (<0.35 mSI) leucogranites highly discordant to the regional host rock structure, and (ii) concordant magnetic fabrics restricted to high susceptibility (>1 mSI) corridors connected to shear zones branching off from Patos. One of these satellite shear zones controlled the syntectonic emplacement of the Serra Redonda pluton, which yields a crystallization age of 576 +/- 3 Ma. This late shearing event marks the peak regional deformation that, south of Patos, was coupled to crustal shortening nearly perpendicular to the shear belt. The chronology of the deformational events indicates that the major shear zones of the eastern Borborema are late structures active after the crustal blocks amalgamated. (C) 2007 Elsevier Ltd. All rights reserved.

A compound class of Weibull and power series distributions

In this paper we introduce the Weibull power series (WPS) class of distributions which is obtained by compounding Weibull and power series distributions where the compounding procedure follows same way that was previously carried out by Adamidis and Loukas (1998) This new class of distributions has as a particular case the two-parameter exponential power series (EPS) class of distributions (Chahkandi and Gawk 2009) which contains several lifetime models such as exponential geometric (Adamidis and Loukas 1998) exponential Poisson (Kus 2007) and exponential logarithmic (Tahmasbi and Rezaei 2008) distributions The hazard function of our class can be increasing decreasing and upside down bathtub shaped among others while the hazard function of an EPS distribution is only decreasing We obtain several properties of the WPS distributions such as moments order statistics estimation by maximum likelihood and inference for a large sample Furthermore the EM algorithm is also used to determine the maximum likelihood estimates of the parameters and we discuss maximum entropy characterizations under suitable constraints Special distributions are studied in some detail Applications to two real data sets are given to show the flexibility and potentiality of the new class of distributions (C) 2010 Elsevier B V All rights reserved