Estimation of Inequality Indices of the Cumulative Distribution Function

Date of Acceptance: 02/03/2015

Activation energy distribution of thermal annealing of a bituminous coal

A bituminous coal was pyrolyzed in a nitrogen stream in an entrained flow reactor at various temperatures from 700 to 1475 degreesC. Char samples were collected at different positions along the reactor. Each collected sample was oxidized nonisothermally in a TGA for reactivity determination. The reactivity of the coal char was found to decrease rapidly with residence time until 0.5 s, after which it decreased only slightly. On the bases of the reactivity data at various temperatures, a new approach was utilized to obtaining the true activation energy distribution function for thermal annealing without the assumption of any distribution function form or a constant preexponential factor. It appears that the true activation energy distribution function consists of two separate parts corresponding to different temperature ranges, suggesting different mechanisms in different temperature ranges. Partially burnt coal chars were also collected along the reactor when the coal was oxidized in air at various temperatures from 700 to 1475 degreesC. The collected samples were analyzed for the residual carbon content and the specific reaction rate was estimated. The characteristic time of thermal deactivation was compared with that of oxidation under realistic conditions. The characteristic times were found to be close to each other, indicating the importance of thermal deactivation during combustion of the coal studied.

A new light on Minkowski's? $(x)$ function

The well--known Minkowski's? $(x)$ function is presented as the asymptotic distribution function of an enumeration of the rationals in (0,1] based on their continued fraction representation. Besides, the singularity of ?$(x)$ is clearly proved in two ways: by exhibiting a set of measure one in which ?ï$(x)$ = 0; and again by actually finding a set of measure one which is mapped onto a set of measure zero and viceversa. These sets are described by means of metrical properties of different systems for real number representation.

Estimating extreme value cumulative distribution functions using bias-corrected kernel approaches

We propose a new kernel estimation of the cumulative distribution function based on transformation and on bias reducing techniques. We derive the optimal bandwidth that minimises the asymptotic integrated mean squared error. The simulation results show that our proposed kernel estimation improves alternative approaches when the variable has an extreme value distribution with heavy tail and the sample size is small.

A generalization of Student’s t-distribution from the viewpoint of special functions

Student’s t-distribution has found various applications in mathematical statistics. One of the main properties of the t-distribution is to converge to the normal distribution as the number of samples tends to infinity. In this paper, by using a Cauchy integral we introduce a generalization of the t-distribution function with four free parameters and show that it converges to the normal distribution again. We provide a comprehensive treatment of mathematical properties of this new distribution. Moreover, since the Fisher F-distribution has a close relationship with the t-distribution, we also introduce a generalization of the F-distribution and prove that it converges to the chi-square distribution as the number of samples tends to infinity. Finally some particular sub-cases of these distributions are considered.

A new study on the power distribution of OFDMA, SC-FDMA and CP-CDMA signals

This paper explores a new technique to calculate and plot the distribution of instantaneous transmit envelope power of OFDMA and SC-FDMA signals from the equation of Probability Density Function (PDF) solved numerically. The Complementary Cumulative Distribution Function (CCDF) of Instantaneous Power to Average Power Ratio (IPAPR) is computed from the structure of the transmit system matrix. This helps intuitively understand the distribution of output signal power if the structure of the transmit system matrix and the constellation used are known. The distribution obtained for OFDMA signal matches complex normal distribution. The results indicate why the CCDF of IPAPR in case of SC-FDMA is better than OFDMA for a given constellation. Finally, with this method it is shown again that cyclic prefixed DS-CDMA system is one case with optimum IPAPR. The insight that this technique provides may be useful in designing area optimised digital and power efficient analogue modules.

Bounds on functionals of the distribution treatment effects

Bounds on the distribution function of the sum of two random variables with known marginal distributions obtained by Makarov (1981) can be used to bound the cumulative distribution function (c.d.f.) of individual treatment effects. Identification of the distribution of individual treatment effects is important for policy purposes if we are interested in functionals of that distribution, such as the proportion of individuals who gain from the treatment and the expected gain from the treatment for these individuals. Makarov bounds on the c.d.f. of the individual treatment effect distribution are pointwise sharp, i.e. they cannot be improved in any single point of the distribution. We show that the Makarov bounds are not uniformly sharp. Specifically, we show that the Makarov bounds on the region that contains the c.d.f. of the treatment effect distribution in two (or more) points can be improved, and we derive the smallest set for the c.d.f. of the treatment effect distribution in two (or more) points. An implication is that the Makarov bounds on a functional of the c.d.f. of the individual treatment effect distribution are not best possible.

The small x behavior of the gluon strucutre function from total cross-sections

Within a QCD-based eikonal model with a dynamical infrared gluon mass scale we discuss how the small x behavior of the gluon distribution function at moderate Q(2) is directly related to the rise of total hadronic cross-sections. In this model the rise of total cross-sections is driven by gluon-gluon semihard scattering processes, where the behavior of the small x gluon distribtuion function exhibits the power law xg(x, Q(2)) = h(Q(2))x(-epsilon). Assuming that the Q(2) scale is proportional to the dynamical gluon mass one, we show that the values of h(Q(2)) obtained in this model are compatible with an earlier result based on a specific nonperturbative Pomeron model. We discuss the implications of this picture for the behavior of input valence-like gluon distributions at low resolution scales.

CLASSICAL DISTRIBUTION-FUNCTIONS DERIVED FROM WIGNER DISTRIBUTION-FUNCTIONS

A mapping which relates the Wigner phase-space distribution function associated with a given stationary quantum-mechanical wavefunction to a specific solution of the time-independent Liouville transport equation is obtained. Two examples are studied.

Mapping Wigner distribution functions into semiclassical distribution functions

A mapping that relates the Wigner phase-space distribution function of a given stationary quantum mechani-cal wave function, a solution of the Schrödinger equation, to a specific solution of the Liouville equation, both subject to the same potential, is studied. By making this mapping, bound states are described by semiclassical distribution functions still depending on Planck's constant, whereas for elastic scattering of a particle by a potential they do not depend on it, the classical limit being reached in this case. Following this method, the mapped distributions of a particle bound in the Pöschl-Teller potential and also in a modified oscillator potential are obtained.

Pion structure function within the instanton model

The leading-twist valence-quark distribution function in the pion is obtained at a low normalization scale of an order of the inverse average size of an instanton pc. The momentum dependent quark mass and the quark-pion vertex are constructed in the framework of the instanton liquid model, using a gauge invariant approach. The parameters of instanton vacuum, the effective instanton radius and quark mass, are related to the vacuum expectation values of the lowest dimension quark-gluon operators and to the pion low energy observables. An analytic expression for the quark distribution function in the pion for a general vertex function is derived. The results are QCD evolved to higher momentum-transfer values, and reasonable agreement with phenomenological analyses of the data on parton distributions for the pion is found. ©2000 The American Physical Society.

The small x behavior of the gluon structure function from total cross-sections

Within a QCD-based eikonal model with a dynamical infrared gluon mass scale we discuss how the small x behavior of the gluon distribution function at moderate Q 2 is directly related to the rise of total hadronic cross-sections. In this model the rise of total cross-sections is driven by gluon-gluon semihard scattering processes, where the behavior of the small x gluon distribution function exhibits the power law xg(x, Q 2) = h(Q 2)x( -∈). Assuming that the Q 2 scale is proportional to the dynamical gluon mass one, we show that the values of h(Q 2) obtained in this model are compatible with an earlier result based on a specific nonperturbative Pomeron model. We discuss the implications of this picture for the behavior of input valence-like gluon distributions at low resolution scales. © 2008 World Scientific Publishing Company.

A new approach to soil classification mapping based on the spatial distribution of soil properties

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

The Truncated Inflated Beta Distribution

The study of proportions is a common topic in many fields of study. The standard beta distribution or the inflated beta distribution may be a reasonable choice to fit a proportion in most situations. However, they do not fit well variables that do not assume values in the open interval (0, c), 0 < c < 1. For these variables, the authors introduce the truncated inflated beta distribution (TBEINF). This proposed distribution is a mixture of the beta distribution bounded in the open interval (c, 1) and the trinomial distribution. The authors present the moments of the distribution, its scoring vector, and Fisher information matrix, and discuss estimation of its parameters. The properties of the suggested estimators are studied using Monte Carlo simulation. In addition, the authors present an application of the TBEINF distribution for unemployment insurance data.

On the Luminous and Dark Matter Distribution in Early-Type Galaxies

The way mass is distributed in galaxies plays a major role in shaping their evolution across cosmic time. The galaxy's total mass is usually determined by tracing the motion of stars in its potential, which can be probed observationally by measuring stellar spectra at different distances from the galactic centre, whose kinematics is used to constrain dynamical models. A class of such models, commonly used to accurately determine the distribution of luminous and dark matter in galaxies, is that of equilibrium models. In this Thesis, a novel approach to the design of equilibrium dynamical models, in which the distribution function is an analytic function of the action integrals, is presented. Axisymmetric and rotating models are used to explain observations of a sample of nearby early-type galaxies in the Calar Alto Legacy Integral Field Area survey. Photometric and spectroscopic data for round and flattened galaxies are well fitted by the models, which are then used to get the galaxies' total mass distribution and orbital anisotropy. The time evolution of massive early-type galaxies is also investigated with numerical models. Their structural properties (mass, size, velocity dispersion) are observed to evolve, on average, with redshift. In particular, they appear to be significantly more compact at higher redshift, at fixed stellar mass, so it is interesting to investigate what drives such evolution. This Thesis focuses on the role played by dark-matter haloes: their mass-size and mass-velocity dispersion correlations evolve similarly to the analogous correlations of ellipticals; at fixed halo mass, the haloes are more compact at higher redshift, similarly to massive galaxies; a simple model, in which all the galaxy's size and velocity-dispersion evolution is due to the cosmological evolution of the underlying halo population, reproduces the observed size and velocity-dispersion of massive compact early-type galaxies up to redshift of about 2.