Bivariate gamma-geometric law and its induced Levy process

In this article we introduce a three-parameter extension of the bivariate exponential-geometric (BEG) law (Kozubowski and Panorska, 2005) [4]. We refer to this new distribution as the bivariate gamma-geometric (BGG) law. A bivariate random vector (X, N) follows the BGG law if N has geometric distribution and X may be represented (in law) as a sum of N independent and identically distributed gamma variables, where these variables are independent of N. Statistical properties such as moment generation and characteristic functions, moments and a variance-covariance matrix are provided. The marginal and conditional laws are also studied. We show that BBG distribution is infinitely divisible, just as the BEG model is. Further, we provide alternative representations for the BGG distribution and show that it enjoys a geometric stability property. Maximum likelihood estimation and inference are discussed and a reparametrization is proposed in order to obtain orthogonality of the parameters. We present an application to a real data set where our model provides a better fit than the BEG model. Our bivariate distribution induces a bivariate Levy process with correlated gamma and negative binomial processes, which extends the bivariate Levy motion proposed by Kozubowski et al. (2008) [6]. The marginals of our Levy motion are a mixture of gamma and negative binomial processes and we named it BMixGNB motion. Basic properties such as stochastic self-similarity and the covariance matrix of the process are presented. The bivariate distribution at fixed time of our BMixGNB process is also studied and some results are derived, including a discussion about maximum likelihood estimation and inference. (C) 2012 Elsevier Inc. All rights reserved.

The geometric Birnbaum-Saunders regression model with cure rate

In this paper, we propose a cure rate survival model by assuming the number of competing causes of the event of interest follows the Geometric distribution and the time to event follow a Birnbaum Saunders distribution. We consider a frequentist analysis for parameter estimation of a Geometric Birnbaum Saunders model with cure rate. Finally, to analyze a data set from the medical area. (C) 2011 Elsevier B.V. All rights reserved.

Radiation balance at the surface in the city of So Paulo, Brazil: diurnal and seasonal variations

The main goal of this work is to describe the diurnal and seasonal variations of the radiation balance components at the surface in the city of So Paulo based on observations carried out during 2004. Monthly average hourly values indicate that the amplitudes of the diurnal cycles of net radiation (Q*), downwelling and upwelling shortwave radiation (SW(DW), SW(UP)), and longwave radiations (LW(DW), LW(UP)) in February were, respectively, 37%, 14%, 19%, 11%, and 5% larger than they were in August. The monthly average daily values indicate a variation of 60% for Q*, with a minimum in June and a maximum in December; 45% for SW(DW), with a minimum in May and a maximum in September; 50% for SW(UP), with a minimum in June and a maximum in September; 13% for LW(DW), with a minimum in July and a maximum in January; and 9% for LW(UP), with a minimum in July and a maximum in February. It was verified that the atmospheric broadband transmissivity varied from 0.36 to 0.57; the effective albedo of the surface varied from 0.08 to 0.10; and the atmospheric effective emissivity varied from 0.79 to 0.92. The surface effective emissivity remained approximately constant and equal to 0.96. The albedo and surface effective emissivity for So Paulo agreed with those reported for urban areas in Europe and North America cities. This indicates that material and geometric effects on albedo and surface emissivity in So Paulo are similar to ones observed in typical middle latitudes cities. On the other hand, it was found that So Paulo city induces an urban heat island with daytime maximum intensity varying from 2.6A degrees C in July (16:00 LT) to 5.5A degrees C in September (15:00 LT). The analysis of the radiometric properties carried out here indicate that this daytime maximum is a primary response to the seasonal variation of daily values of net solar radiation at the surface.

GEOMETRIC RELATIONS BETWEEN SPACES OF NUCLEAR OPERATORS AND SPACES OF COMPACT OPERATORS

We extend and provide a vector-valued version of some results of C. Samuel about the geometric relations between the spaces of nuclear operators N(E, F) and spaces of compact operators K(E, F), where E and F are Banach spaces C(K) of all continuous functions defined on the countable compact metric spaces K equipped with the supremum norm. First we continue Samuel's work by proving that N(C(K-1), C(K-2)) contains no subspace isomorphic to K(C(K-3), C(K-4)) whenever K-1, K-2, K-3 and K-4 are arbitrary infinite countable compact metric spaces. Then we show that it is relatively consistent with ZFC that the above result and the main results of Samuel can be extended to C(K-1, X), C(K-2,Y), C(K-3, X) and C(K-4, Y) spaces, where K-1, K-2, K-3 and K-4 are arbitrary infinite totally ordered compact spaces; X comprises certain Banach spaces such that X* are isomorphic to subspaces of l(1); and Y comprises arbitrary subspaces of l(p), with 1 < p < infinity. Our results cover the cases of some non-classical Banach spaces X constructed by Alspach, by Alspach and Benyamini, by Benyamini and Lindenstrauss, by Bourgain and Delbaen and also by Argyros and Haydon.

Average control of Markov decision processes with Feller transition probabilities and general action spaces

This paper studies the average control problem of discrete-time Markov Decision Processes (MDPs for short) with general state space, Feller transition probabilities, and possibly non-compact control constraint sets A(x). Two hypotheses are considered: either the cost function c is strictly unbounded or the multifunctions A(r)(x) = {a is an element of A(x) : c(x, a) <= r} are upper-semicontinuous and compact-valued for each real r. For these two cases we provide new results for the existence of a solution to the average-cost optimality equality and inequality using the vanishing discount approach. We also study the convergence of the policy iteration approach under these conditions. It should be pointed out that we do not make any assumptions regarding the convergence and the continuity of the limit function generated by the sequence of relative difference of the alpha-discounted value functions and the Poisson equations as often encountered in the literature. (C) 2012 Elsevier Inc. All rights reserved.

Probing the anomalous extinction of four young star clusters: the use of colour-excess, main-sequence fitting and fractal analysis

Aims. We studied four young star clusters to characterise their anomalous extinction or variable reddening and asses whether they could be due to contamination by either dense clouds or circumstellar effects. Methods. We evaluated the extinction law (R-V) by adopting two methods: (i) the use of theoretical expressions based on the colour-excess of stars with known spectral type; and (ii) the analysis of two-colour diagrams, where the slope of the observed colour distribution was compared to the normal distribution. An algorithm to reproduce the zero-age main-sequence (ZAMS) reddened colours was developed to derive the average visual extinction (A(V)) that provides the closest fit to the observational data. The structure of the clouds was evaluated by means of a statistical fractal analysis, designed to compare their geometric structure with the spatial distribution of the cluster members. Results. The cluster NGC 6530 is the only object of our sample affected by anomalous extinction. On average, the other clusters suffer normal extinction, but several of their members, mainly in NGC 2264, seem to have high R-V, probably because of circumstellar effects. The ZAMS fitting provides A(V) values that are in good agreement with those found in the literature. The fractal analysis shows that NGC 6530 has a centrally concentrated distribution of stars that differs from the substructures found in the density distribution of the cloud projected in the A(V) map, suggesting that the original cloud was changed by the cluster formation. However, the fractal dimension and statistical parameters of Berkeley 86, NGC 2244, and NGC 2264 indicate that there is a good cloud-cluster correlation, when compared to other works based on an artificial distribution of points.

Geometrical and kinematic properties of interfacial waves in stratified oil-water flow in inclined pipe

The stratified oil-water flow pattern is common in the petroleum industry, especially in offshore directional wells and pipelines. Previous studies have shown that the phenomenon of flow pattern transition in stratified flow can be related to the interfacial wave structure (problem of hydrodynamic instability). The study of the wavy stratified flow pattern requires the characterization of the interfacial wave properties, i.e., average shape, celerity and geometric properties (amplitude and wavelength) as a function of holdup, inclination angle and phases' relative velocity. However, the data available in the literature on wavy stratified flow is scanty, especially in inclined pipes and when oil is viscous. This paper presents new geometric and kinematic interfacial wave properties as a function of a proposed two-phase Froude number in the wavy-stratified liquid-liquid flow. The experimental work was conducted in a glass test line of 12 m and 0.026 m id., oil (density and viscosity of 828 kg/m(3) and 0.3 Pa s at 20 degrees C, respectively) and water as the working fluids at several inclinations from horizontal (-20 degrees, -10 degrees, 0 degrees, 10 degrees, 20 degrees). The results suggest a physical relation between wave shape and the hydrodynamic stability of the stratified liquid-liquid flow pattern. (C) 2011 Elsevier Inc. All rights reserved.

Bird species diversity in the Atlantic Forest of Brazil is not explained by the Mid-domain Effect

The Atlantic Forest is an excellent case study for the elevational diversity of birds, and some inventories along elevational gradients have been carried out in Brazil. Since none of these studies explain the patterns of species richness with elevation, we herein review all Brazilian studies on bird elevational diversity, and test a geometric constraint null model that predicts a unimodal species-altitude curve, the Mid-domain Effect (MDE). We searched for bird inventories in the literature and also analysed our own survey data using limited-radius point counts along an 800 m elevational gradient in the state of São Paulo, Brazil. We found 10 investigations of elevational diversity of Atlantic Forest birds and identified five different elevational patterns: monotonic decreasing diversity, constant at low elevations, constant at low elevations but increasing towards the middle, and two undescribed patterns for Atlantic Forest birds, trough-shaped and increasing diversity. The average MDE fit was low (r² = 0.31) and none of the MDE predictions were robust across all gradients. Those studies with good MDE model fits had obvious sampling bias. Although it has been proposed that the MDE may be positively associated with the elevational diversity of birds, it does not fit the Brazilian Atlantic Forest bird elevational diversity.