Fast parallel $$\alpha $$-stable distribution function evaluation and parameter estimation using OpenCL in GPGPUs

\(\alpha \)-Stable distributions are a family of probability distributions found to be suitable to model many complex processes and phenomena in several research fields, such as medicine, physics, finance and networking, among others. However, the lack of closed expressions makes their evaluation analytically intractable, and alternative approaches are computationally expensive. Existing numerical programs are not fast enough for certain applications and do not make use of the parallel power of general purpose graphic processing units. In this paper, we develop novel parallel algorithms for the probability density function and cumulative distribution function—including a parallel Gauss–Kronrod quadrature—, quantile function, random number generator and maximum likelihood estimation of \(\alpha \)-stable distributions using OpenCL, achieving significant speedups and precision in all cases. Thanks to the use of OpenCL, we also evaluate the results of our library with different GPU architectures.     

The effects of immigration on children in the Mexican-American community

Effects of immigration on Mexican-American immigrant children and families can be lifelong. This article describes conditions contributing to immigration and its effects on poor families, describing and illustrating developmental disruptions, and emphasizing effects on school participation and family dynamics.He is a graduate of the Illinois School of Professional Psychology, and has clinical and supervisory experience in child welfare.     

A New Look at Half-normal Plots for Assessing the Significance of Contrasts for Unreplicated Factorials

The visual inspection of a half-normal plot is a popular procedure for interpreting data from unreplicated factorial experiments. As this technique is somewhat subjective, the plot should preferably be supplemented with a more formal procedure. However, despite the improvements proposed by Zahn, the formal method using the half-normal plot suggested by Daniel seems to be rarely used. We investigate this procedure by using simulations and real data and suggest a modification to improve its acceptability. We also present corrected critical values for a procedure proposed by Lenth which was found to be miscalibrated.     

The Cornish-Fisher expansion for a class of statistics in first order autoregression

ABSTRACT

This article is concerned with the derivation and study of the Cornish-Fisher expansion for a wide class of estimators of the parameter in the first order autoregressive process. Second and third order Cornish-Fisher approximations to the quantile of the distribution of the corresponding asymptotically normal standardized statistic are stated explicitly and their accuracy is examined, both theoretically and numerically, by comparing them with the exact value of the quantile obtained by Monte Carlo simulation.     

Dependence Between Two Diagnostic Tests with Copula Function Approach: A Simulation Study

The study of the dependence between two medical diagnostic tests is an important issue in health research since it can modify the diagnosis and, therefore, the decision regarding a therapeutic treatment for an individual. In many practical situations, the diagnostic procedure includes the use of two tests, with outcomes on a continuous scale. For final classification, usually there is an additional “gold standard” or reference test. Considering binary test responses, we usually assume independence between tests or a joint binary structure for dependence. In this article, we introduce a simulation study assuming two dependent dichotomized tests using two copula function dependence structures in the presence or absence of verification bias. We compare the test parameter estimators obtained under copula structure dependence with those obtained assuming binary dependence or assuming independent tests.     

Are the Order Statistics Ordered? A Survey of Recent Results

The distributions of coherent systems with components with exchangeable lifetimes can be represented as mixtures of distributions of order statistics (k-out-of-n systems) from possibly dependent samples by using the concept of the signature of Samaniego (1985 Samaniego , F. ( 1985 ). On closure of the IFR class under formation of coherent systems . IEEE Trans. Reliabil. R-34 : 69 – 72 .[Crossref], [Web of Science ®] , [Google Scholar]). This representation, together with Rychlik's (1993 Rychlik , T. ( 1993 ). Bounds for expectation of L-estimates for dependent samples . Statistics 24 : 1 – 7 .[Taylor & Francis Online] , [Google Scholar]) results, can be used to obtain sharp bounds on the distribution (or the reliability) function and on the expected lifetime of the system. Also, this representation can be used to determine the asymptotic behavior of the hazard rate of the system when the order statistics are ordered in the hazard rate order. Moreover, the lifetime distributions of coherent systems (and in particular, of order statistics) can also be represented as generalized mixtures (that is, mixtures with some negative weights) of distributions of series system lifetimes by using the concept of the minimal signature defined by Navarro et al. (2007a Navarro , J. , Ruiz , J. M. , Sandoval , C. J. ( 2007a ). Properties of coherent systems with dependent components . Commun. Statist. Theory Methods 36 : 175 – 191 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). This representation can also be used to determine the final behavior of the hazard rate of the system through the behavior of the hazard rate of the series systems. In particular, it can be used to show that the order statistics are, under some conditions, asymptotically hazard rate ordered. However, in general, this result is not true, that is, the order statistics need not be hazard rate ordered.     

A Bayesian analysis for the Block and Basu bivariate exponential distribution in the presence of covariates and censored data

In this paper, we introduce a Bayesian Analysis for the Block and Basu bivariate exponential distribution using Markov Chain Monte Carlo (MCMC) methods and considering lifetimes in presence of covariates and censored data. Posterior summaries of interest are obtained using the popular WinBUGS software. Numerical illustrations are introduced considering a medical data set related to the recurrence times of infection for kidney patients and a medical data set related to bone marrow transplantation for leukemia.     

An empirical comparison of Canonical Correspondence Analysis and STATICO in the identification of spatio-temporal ecological relationships

The wide-ranging and rapidly evolving nature of ecological studies mean that it is not possible to cover all existing and emerging techniques for analyzing multivariate data. However, two important methods enticed many followers: the Canonical Correspondence Analysis (CCA) and the STATICO analysis. Despite the particular characteristics of each, they have similarities and differences, which when analyzed properly, can, together, provide important complementary results to those that are usually exploited by researchers. If on one hand, the use of CCA is completely generalized and implemented, solving many problems formulated by ecologists, on the other hand, this method has some weaknesses mainly caused by the imposition of the number of variables that is required to be applied (much higher in comparison with samples). Also, the STATICO method has no such restrictions, but requires that the number of variables (species or environment) is the same in each time or space. Yet, the STATICO method presents information that can be more detailed since it allows visualizing the variability within groups (either in time or space). In this study, the data needed for implementing these methods are sketched, as well as the comparison is made showing the advantages and disadvantages of each method. The treated ecological data are a sequence of pairs of ecological tables, where species abundances and environmental variables are measured at different, specified locations, over the course of time.     

Therapeutic residential care in Spain. Population treated and therapeutic coverage

Therapeutic residential care (TRC) is the name given to specialized children's homes for treating cases with severe emotional and behavioural problems that have been placed in residential care. A recent international review has revealed great diversity in the referral criteria of cases and in the models of intervention carried out. The goal of this study is to describe the population treated in these types of facilities in Spain and the therapeutic coverage given. The sample is made up of 215 young people in children's homes, of whom 93 are in TRC. The cases referred to TRC have been in residential care for less time but have gone through a greater number of placements. These young people also exhibit more problems of drug use, and there is a larger percentage of clinical‐range cases in the Child Behaviour Checklist scales of attention problems and aggressive behaviour. Nevertheless, the results of logistic regression indicate that the only variables that significantly increase the probability of being referred to TRC are drug use and changes of care placements. With regard to therapeutic care, there is a higher percentage in the TRC group receiving psychiatric care, and the sessions are also more frequent.