The new class of Kummer beta generalized distributions

Ng and Kotz (1995) introduced a distribution that provides greater flexibility to extremes. We define and study a new class of distributions called the Kummer beta generalized family to extend the normal, Weibull, gamma and Gumbel distributions, among several other well-known distributions. Some special models are discussed. The ordinary moments of any distribution in the new family can be expressed as linear functions of probability weighted moments of the baseline distribution. We examine the asymptotic distributions of the extreme values. We derive the density function of the order statistics, mean absolute deviations and entropies. We use maximum likelihood estimation to fit the distributions in the new class and illustrate its potentiality with an application to a real data set.

A new long-term lifetime distribution induced by a latent complementary risk framework

In this paper, we proposed a new three-parameter long-term lifetime distribution induced by a latent complementary risk framework with decreasing, increasing and unimodal hazard function, the long-term complementary exponential geometric distribution. The new distribution arises from latent competing risk scenarios, where the lifetime associated scenario, with a particular risk, is not observable, rather we observe only the maximum lifetime value among all risks, and the presence of long-term survival. The properties of the proposed distribution are discussed, including its probability density function and explicit algebraic formulas for its reliability, hazard and quantile functions and order statistics. The parameter estimation is based on the usual maximum-likelihood approach. A simulation study assesses the performance of the estimation procedure. We compare the new distribution with its particular cases, as well as with the long-term Weibull distribution on three real data sets, observing its potential and competitiveness in comparison with some usual long-term lifetime distributions.

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.

Size distributions and temporal variations of biological aerosol particles in the Amazon rainforest characterized by microscopy and real-time UV-APS fluorescence techniques during AMAZE-08

As a part of the AMAZE-08 campaign during the wet season in the rainforest of central Amazonia, an ultraviolet aerodynamic particle sizer (UV-APS) was operated for continuous measurements of fluorescent biological aerosol particles (FBAP). In the coarse particle size range (> 1 mu m) the campaign median and quartiles of FBAP number and mass concentration were 7.3x10(4) m(-3) (4.0-13.2x10(4) m(-3)) and 0.72 mu g m(-3) (0.42-1.19 mu g m(-3)), respectively, accounting for 24% (11-41%) of total particle number and 47% (25-65%) of total particle mass. During the five-week campaign in February-March 2008 the concentration of coarse-mode Saharan dust particles was highly variable. In contrast, FBAP concentrations remained fairly constant over the course of weeks and had a consistent daily pattern, peaking several hours before sunrise, suggesting observed FBAP was dominated by nocturnal spore emission. This conclusion was supported by the consistent FBAP number size distribution peaking at 2.3 mu m, also attributed to fungal spores and mixed biological particles by scanning electron microscopy (SEM), light microscopy and biochemical staining. A second primary biological aerosol particle (PBAP) mode between 0.5 and 1.0 mu m was also observed by SEM, but exhibited little fluorescence and no true fungal staining. This mode may have consisted of single bacterial cells, brochosomes, various fragments of biological material, and small Chromalveolata (Chromista) spores. Particles liquid-coated with mixed organic-inorganic material constituted a large fraction of observations, and these coatings contained salts likely from primary biological origin. We provide key support for the suggestion that real-time laser-induce fluorescence (LIF) techniques using 355 nm excitation provide size-resolved concentrations of FBAP as a lower limit for the atmospheric abundance of biological particles in a pristine environment. We also show some limitations of using the instrument for ambient monitoring of weakly fluorescent particles < 2 mu m. Our measurements confirm that primary biological particles, fungal spores in particular, are an important fraction of supermicron aerosol in the Amazon and that may contribute significantly to hydrological cycling, especially when coated by mixed inorganic material.

Generalized beta-generated distributions

This article introduces generalized beta-generated (GBG) distributions. Sub-models include all classical beta-generated, Kumaraswamy-generated and exponentiated distributions. They are maximum entropy distributions under three intuitive conditions, which show that the classical beta generator skewness parameters only control tail entropy and an additional shape parameter is needed to add entropy to the centre of the parent distribution. This parameter controls skewness without necessarily differentiating tail weights. The GBG class also has tractable properties: we present various expansions for moments, generating function and quantiles. The model parameters are estimated by maximum likelihood and the usefulness of the new class is illustrated by means of some real data sets. (c) 2011 Elsevier B.V. All rights reserved.

A Homonuclear Rotational Echo Double-Resonance Method for Measuring Site-Resolved Distance Distributions in I=1/2 Spin Pairs, Clusters, and Multispin Systems

Deutsche Forschungsgemeinschaft [SFB 858]

Levy stable distributions via associated integral transform

We present a method of generation of exact and explicit forms of one-sided, heavy-tailed Levy stable probability distributions g(alpha)(x), 0 <= x < infinity, 0 < alpha < 1. We demonstrate that the knowledge of one such a distribution g a ( x) suffices to obtain exactly g(alpha)p ( x), p = 2, 3, .... Similarly, from known g(alpha)(x) and g(beta)(x), 0 < alpha, beta < 1, we obtain g(alpha beta)( x). The method is based on the construction of the integral operator, called Levy transform, which implements the above operations. For a rational, alpha = l/k with l < k, we reproduce in this manner many of the recently obtained exact results for g(l/k)(x). This approach can be also recast as an application of the Efros theorem for generalized Laplace convolutions. It relies solely on efficient definite integration. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4709443]

Sets of probability distributions, independence, and convexity

This paper analyzes concepts of independence and assumptions of convexity in the theory of sets of probability distributions. The starting point is Kyburg and Pittarelli's discussion of "convex Bayesianism" (in particular their proposals concerning E-admissibility, independence, and convexity). The paper offers an organized review of the literature on independence for sets of probability distributions; new results on graphoid properties and on the justification of "strong independence" (using exchangeability) are presented. Finally, the connection between Kyburg and Pittarelli's results and recent developments on the axiomatization of non-binary preferences, and its impact on "complete" independence, are described.

Quantum deformation of the angular distributions of synchrotron radiation. Emission from particles in the first excited state

The exact expressions for the characteristics of synchrotron radiation of charged particles in the first excited state are obtained in analytical form using quantum theory methods. We performed a detailed analysis of the angular distribution structure of radiation power and its polarization for particles with spin 0 and 1/2. It is shown that the exact quantum calculations lead to results that differ substantially from the predictions of classical theory.

Likelihood-based inference for power distributions

This paper considers likelihood-based inference for the family of power distributions. Widely applicable results are presented which can be used to conduct inference for all three parameters of the general location-scale extension of the family. More specific results are given for the special case of the power normal model. The analysis of a large data set, formed from density measurements for a certain type of pollen, illustrates the application of the family and the results for likelihood-based inference. Throughout, comparisons are made with analogous results for the direct parametrisation of the skew-normal distribution.

An evaluation of the distributions of polychlorinated biphenyls and organic matter in coastal sediments

The objective of this thesis is to improve the understanding of what processes and mechanism affects the distribution of polychlorinated biphenyls (PCBs) and organic carbon in coastal sediments. Because of the strong association of hydrophobic organic contaminants (HOCs) such as PCBs with organic matter in the aquatic environment, these two entities are naturally linked. The coastal environment is the most complex and dynamic part of the ocean when it comes to both cycling of organic matter and HOCs. This environment is characterised by the largest fluxes and most diverse sources of both entities. A wide array of methods was used to study these processes throughout this thesis. In the field sites in the Stockholm archipelago of the Baltic proper, bottom sediments and settling particulate matter were retrieved using sediment coring devices and sediment traps from morphometrically and seismically well-characterized locations. In the laboratory, the samples have been analysed for PCBs, stable carbon isotope ratios, carbon-nitrogen atom ratios as well as standard sediment properties. From the fieldwork in the Stockholm Archipelago and the following laboratory work it was concluded that the inner Stockholm archipelago has a low (≈ 4%) trapping efficiency for freshwater-derived organic carbon. The corollary is a large potential for long-range waterborne transport of OC and OC-associated nutrients and hydrophobic organic pollutants from urban Stockholm to more pristine offshore Baltic Sea ecosystems. Theoretical work has been carried out using Geographical Information Systems (GIS) and statistical methods on a database of 4214 individual sediment samples, each with reported individual PCB congener concentrations. From this work it was concluded that the continental shelf sediments are key global inventories and ultimate sinks of PCBs. Depending on congener, 10-80% of the cumulative historical emissions to the environment are accounted for in continental shelf sediments. Further it was concluded that the many infamous and highly contaminated surface sediments of urban harbours and estuaries of contaminated rivers cannot be of importance as a secondary source to sustain the concentrations observed in remote sediments. Of the global shelf PCB inventory < 1% are in sediments near population centres while ≥ 90% is in remote areas (> 10 km from any dwellings). The remote sub-basin of the North Atlantic Ocean contains approximately half of the global shelf sediment inventory for most of the PCBs studied.

Database of diazotrophs in global ocean: abundances, biomass and nitrogen fixation rates

[EN] Marine N2 fixing microorganisms, termed diazotrophs, are a key functional group in marine pelagic ecosystems. The biological fixation of dinitrogen (N2) to bioavailable nitrogen provides an important new source of nitrogen for pelagic marine ecosystems 5 and influences primary productivity and organic matter export to the deep ocean. As one of a series of efforts to collect biomass and rates specific to different phytoplankton functional groups, we have constructed a database on diazotrophic organisms in the global pelagic upper ocean by compiling about 12 000 direct field measurements of cyanobacterial diazotroph abundances (based on microscopic cell counts or qPCR 10 assays targeting the nifH genes) and N2 fixation rates. Biomass conversion factors are estimated based on cell sizes to convert  abundance data to diazotrophic biomass. The database is limited spatially, lacking large regions of the ocean especially in the Indian Ocean. The data are approximately log-normal distributed, and large variances exist in most sub-databases with non-zero values differing 5 to 8 orders of magnitude. 15 Lower mean N2 fixation rate was found in the North Atlantic Ocean than the Pacific Ocean. Reporting the geometric mean and the range of one geometric standard error below and above the geometric mean, the pelagic N2 fixation rate in the global ocean is estimated to be 62 (53–73) TgNyr−1 and the pelagic diazotrophic biomass in the global ocean is estimated to be 4.7 (2.3–9.6) TgC from cell counts and to 89 (40–20 200) TgC from nifH-based abundances. Uncertainties related to biomass conversion factors can change the estimate of geometric mean pelagic diazotrophic biomass in the global ocean by about ±70 %. This evolving database can be used to study spatial and temporal distributions and variations of marine N2 fixation, to validate geochemical estimates and to parameterize and validate biogeochemical models. The database is 25 stored in PANGAEA (http://doi.pangaea.de/10.1594/PANGAEA.774851).

Meridional changes in water mass distributions off NW Africa during November 2007/2008

[EN] An optimum multiparameter analysis was applied to a data set for the eastern boundary of the North Atlantic subtropical gyre, gathered during November of two consecutive years and spanning from 16 to 36º N. This data set covers over 20º of latitude with good meridional and zonal resolution over the whole coastal transition zone. The contribution from six water types in the depth range between 100 and 2000 m is solved. In the 100 to 700 m depth range the central waters of southern and northern origin meet abruptly at the Cape Verde Frontal Zone. This front traditionally has been reported to stretch from Cape Blanc, at about 21.5º N, to the Cape Verde Islands, but in our case it penetrates as far as 24º N over the continental slope. South of 21º N latitude we actually find a less saline and more oxygenated variety of South Atlantic Central Water, which we ascribe to less diluted equatorial waters. In the 700 to 1500 m depth range the dominant water type is a diluted form of Antarctic Intermediate Water (AAIW), whose influence smoothly disappears north of the Canary Islands as it is replaced by Mediterranean Water (MW); at latitudes where both water masses coexist, we observe MW offshore while AAIW is found near-shore. North Atlantic Deep Water is the dominating water type below about 1300/1700 m depth south/north of the Canary Islands; this abrupt change in depth suggests the existence of different paths for the deep waters reaching both sides of the archipelago.