A new family of generalized distributions

Kumaraswamy [Generalized probability density-function for double-bounded random-processes, J. Hydrol. 462 (1980), pp. 79-88] introduced a distribution for double-bounded random processes with hydrological applications. For the first time, based on this distribution, we describe a new family of generalized distributions (denoted with the prefix `Kw`) to extend the normal, Weibull, gamma, Gumbel, inverse Gaussian distributions, among several well-known distributions. Some special distributions in the new family such as the Kw-normal, Kw-Weibull, Kw-gamma, Kw-Gumbel and Kw-inverse Gaussian distribution are discussed. We express the ordinary moments of any Kw generalized distribution as linear functions of probability weighted moments (PWMs) of the parent distribution. We also obtain the ordinary moments of order statistics as functions of PWMs of the baseline distribution. We use the method of maximum likelihood to fit the distributions in the new class and illustrate the potentiality of the new model with an application to real data.

The complementary exponential geometric distribution: Model, properties, and a comparison with its counterpart

In this paper, we proposed a new two-parameter lifetime distribution with increasing failure rate, the complementary exponential geometric distribution, which is complementary to the exponential geometric model proposed by Adamidis and Loukas (1998). The new distribution arises on a latent complementary risks scenario, in which the lifetime associated with a particular risk is not observable; rather, we observe only the maximum lifetime value among all risks. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulas for its reliability and failure rate functions, moments, including the mean and variance, variation coefficient, and modal value. The parameter estimation is based on the usual maximum likelihood approach. We report the results of a misspecification simulation study performed in order to assess the extent of misspecification errors when testing the exponential geometric distribution against our complementary one in the presence of different sample size and censoring percentage. The methodology is illustrated on four real datasets; we also make a comparison between both modeling approaches. (C) 2011 Elsevier B.V. All rights reserved.

Parametric analysis of discrepant sets of data

In this paper a new parametric method to deal with discrepant experimental results is developed. The method is based on the fit of a probability density function to the data. This paper also compares the characteristics of different methods used to deduce recommended values and uncertainties from a discrepant set of experimental data. The methods are applied to the (137)Cs and (90)Sr published half-lives and special emphasis is given to the deduced confidence intervals. The obtained results are analyzed considering two fundamental properties expected from an experimental result: the probability content of confidence intervals and the statistical consistency between different recommended values. The recommended values and uncertainties for the (137)Cs and (90)Sr half-lives are 10,984 (24) days and 10,523 (70) days, respectively. (C) 2009 Elsevier B.V. All rights reserved.

DENSITY PROFILE, VELOCITY ANISOTROPY, AND LINE-OF-SIGHT EXTERNAL CONVERGENCE OF SLACS GRAVITATIONAL LENSES

Data from 58 strong-lensing events surveyed by the Sloan Lens ACS Survey are used to estimate the projected galaxy mass inside their Einstein radii by two independent methods: stellar dynamics and strong gravitational lensing. We perform a joint analysis of these two estimates inside models with up to three degrees of freedom with respect to the lens density profile, stellar velocity anisotropy, and line-of-sight (LOS) external convergence, which incorporates the effect of the large-scale structure on strong lensing. A Bayesian analysis is employed to estimate the model parameters, evaluate their significance, and compare models. We find that the data favor Jaffe`s light profile over Hernquist`s, but that any particular choice between these two does not change the qualitative conclusions with respect to the features of the system that we investigate. The density profile is compatible with an isothermal, being sightly steeper and having an uncertainty in the logarithmic slope of the order of 5% in models that take into account a prior ignorance on anisotropy and external convergence. We identify a considerable degeneracy between the density profile slope and the anisotropy parameter, which largely increases the uncertainties in the estimates of these parameters, but we encounter no evidence in favor of an anisotropic velocity distribution on average for the whole sample. An LOS external convergence following a prior probability distribution given by cosmology has a small effect on the estimation of the lens density profile, but can increase the dispersion of its value by nearly 40%.

Shared information in stationary states at criticality

We consider bipartitions of one-dimensional extended systems whose probability distribution functions describe stationary states of stochastic models. We define estimators of the information shared between the two subsystems. If the correlation length is finite, the estimators stay finite for large system sizes. If the correlation length diverges, so do the estimators. The definition of the estimators is inspired by information theory. We look at several models and compare the behaviors of the estimators in the finite-size scaling limit. Analytical and numerical methods as well as Monte Carlo simulations are used. We show how the finite-size scaling functions change for various phase transitions, including the case where one has conformal invariance.

Density profiles in the raise and peel model with and without a wall; physics and combinatorics

We consider the raise and peel model of a one-dimensional fluctuating interface in the presence of an attractive wall. The model can also describe a pair annihilation process in disordered unquenched media with a source at one end of the system. For the stationary states, several density profiles are studied using Monte Carlo simulations. We point out a deep connection between some profiles seen in the presence of the wall and in its absence. Our results are discussed in the context of conformal invariance ( c = 0 theory). We discover some unexpected values for the critical exponents, which are obtained using combinatorial methods. We have solved known ( Pascal`s hexagon) and new (split-hexagon) bilinear recurrence relations. The solutions of these equations are interesting in their own right since they give information on certain classes of alternating sign matrices.

Bayesian density estimation using Skew Student-t-Normal mixtures

We present a Bayesian approach for modeling heterogeneous data and estimate multimodal densities using mixtures of Skew Student-t-Normal distributions [Gomez, H.W., Venegas, O., Bolfarine, H., 2007. Skew-symmetric distributions generated by the distribution function of the normal distribution. Environmetrics 18, 395-407]. A stochastic representation that is useful for implementing a MCMC-type algorithm and results about existence of posterior moments are obtained. Marginal likelihood approximations are obtained, in order to compare mixture models with different number of component densities. Data sets concerning the Gross Domestic Product per capita (Human Development Report) and body mass index (National Health and Nutrition Examination Survey), previously studied in the related literature, are analyzed. (c) 2008 Elsevier B.V. All rights reserved.