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Volume 39 (2), July-December 2015

  • Twenty years of P-splines (invited article)

    Paul H.C. Eilers, Brian D. Marx and Maria Durbán

    Abstract: P-splines first appeared in the limelight twenty years ago. Since then they have become popular in applications and in theoretical work. The combination of a rich B-spline basis and a simple difference penalty lends itself well to a variety of generalizations, because it is based on regression. In effect, P-splines allow the building of a “backbone” for the “mixing and matching” of a variety of additive smooth structure components, while inviting all sorts of extensions: varying-coefficient effects, signal (functional) regressors, two-dimensional surfaces, non-normal responses, quantile (expectile) modelling, among others. Strong connections with mixed models and Bayesian analysis have been established. We give an overview of many of the central developments during the first two decades of P-splines.

    Keywords: B-splines, penalty, additive model, mixed model, multidimensional smoothing.

    Pages: 149–186

  • Likelihood-based inference for the power regression model

    Guillermo Martínez-Flórez, Heleno Bolfarine and Héctor W. Gómez

    Abstract: In this paper we investigate an extension of the power-normal model, called the alpha-power model and specialize it to linear and nonlinear regression models, with and without correlated errors. Maximum likelihood estimation is considered with explicit derivation of the observed and expected Fisher information matrices. Applications are considered for the Australian athletes data set and also to a data set studied in Xie et al. (2009). The main conclusion is that the proposed model can be a viable alternative in situations were the normal distribution is not the most adequate model.

    Keywords: Correlation, maximum likelihood, power-normal distribution, regression.

    Pages: 187–208

  • On the bivariate Sarmanov distribution and copula. An application on insurance data using truncated marginal distributions

    Zuhair Bahraoui, Catalina Bolancé, Elena Pelican and Raluca Vernic

    Abstract: The Sarmanov family of distributions can provide a good model for bivariate random variables and it is used to model dependency in a multivariate setting with given marginals. In this paper, we focus our attention on the bivariate Sarmanov distribution and copula with different truncated extreme value marginal distributions. We compare a global estimation method based on maximizing the full log-likelihood function with the estimation based on maximizing the pseudo-log-likelihood function for copula (or partial estimation). Our aim is to estimate two statistics that can be used to evaluate the risk of the sum exceeding a given value. Numerical results using a real data set from the motor insurance sector are presented.

    Keywords: Bivariate Sarmanov distribution, truncated marginal distributions, copula representation, risk measures.

    Pages: 209–230

  • On the interpretation of differences between groups for compositional data

    Josep-Antoni Martín-Fernández, Josep Daunis-i-Estadella and Glòria Mateu-Figueras

    Abstract: Social polices are designed using information collected in surveys; such as the Catalan Time Use survey. Accurate comparisons of time use data among population groups are commonly analysed using statistical methods. The total daily time expended on different activities by a single person is equal to 24 hours. Because this type of data are compositional, its sample space has particular properties that statistical methods should respect. The critical points required to interpret differences between groups are provided and described in terms of log-ratio methods. These techniques facilitate the interpretation of the relative differences detected in multivariate and univariate analysis.

    Keywords: Log-ratio transformations, MANOVA, perturbation, simplex, subcomposition.

    Pages: 231–252

  • Robust project management with the tilted beta distribution

    Eugene D. Hahn and María del Mar López Martín

    Abstract: Recent years have seen an increase in the development of robust approaches for stochastic project management methodologies such as PERT (Program Evaluation and Review Technique). These robust approaches allow for elevated likelihoods of outlying events, thereby widening interval estimates of project completion times. However, little attention has been paid to the fact that outlying events and/or expert judgments may be asymmetric. We propose the tilted beta distribution which permits both elevated likelihoods of outlying events as well as an asymmetric representation of these events. We examine the use of the tilted beta distribution in PERT with respect to other project management distributions.

    Keywords: Activity times, finite mixture, PERT, tilted beta distribution, robust project management, sensitivity analysis.

    Pages: 253–272

  • A note on "Double bounded Kumaraswamy-power series class of distributions"

    Tibor K. Pogány and Saralees Nadarajah

    Abstract: In a recent edition of SORT, Bidram and Nekoukhou proposed a novel class of distributions and derived its mathematical properties. Several of the mathematical properties are expressed as single infinite sums or double infinite sums. Here, we show that many of these properties can be expressed in terms of known special functions, functions for which in-built routines are widely available.

    Keywords: Double bounded Kumaraswamy-power series class of distributions, Fox Wright generalized, hypergeometric function, generalized hypergeometric function.

    Pages: 273–280

  • Parameter estimation of Poisson generalized linear mixed models based on three different statistical principles: a simulation study

    Martí Casals, Klaus Langohr, Josep Lluís Carrasco and Lars Rönnegård

    Abstract: Generalized linear mixed models are flexible tools for modeling non-normal data and are useful for accommodating overdispersion in Poisson regression models with random effects. Their main difficulty resides in the parameter estimation because there is no analytic solution for the maximization of the marginal likelihood. Many methods have been proposed for this purpose and many of them are implemented in software packages. The purpose of this study is to compare the performance of three different statistical principles —marginal likelihood, extended likelihood, Bayesian analysis— via simulation studies. Real data on contact wrestling are used for illustration.

    Keywords: Estimation methods, overdispersion, Poisson generalized linear mixed models, simulation study, statistical principles, sport injuries.

    Pages: 281–308

  • Multinomial logistic estimation in dual frame surveys

    David Molina, Maria del Mar Rueda, Antonio Arcos and Maria Giovanna Ranalli

    Abstract: We consider estimation techniques from dual frame surveys in the case of estimation of proportions when the variable of interest has multinomial outcomes. We propose to describe the joint distribution of the class indicators by a multinomial logistic model. Logistic generalized regression estimators and model calibration estimators are introduced for class frequencies in a population. Theoretical asymptotic properties of the proposed estimators are shown and discussed. Monte Carlo experiments are also carried out to compare the efficiency of the proposed procedures for finite size samples and in the presence of different sets of auxiliary variables. The simulation studies indicate that the multinomial logistic formulation yields better results than the classical estimators that implicitly assume individual linear models for the variables. The proposed methods are also applied in an attitude survey.

    Keywords: Finite population, survey sampling, auxiliary information, model assisted inference, calibration.

    Pages: 309–336

Volume 39 (1), January-June 2015

  • Inference on the parameters of the Weibull distribution using records

    Ali Akbar Jafari and Hojatollah Zakerzadeh

    Abstract: The Weibull distribution is a very applicable model for lifetime data. In this paper, we have investigated inference on the parameters of Weibull distribution based on record values. We first propose a simple and exact test and a confidence interval for the shape parameter. Then, in addition to a generalized confidence interval, a generalized test variable is derived for the scale parameter when the shape parameter is unknown. The paper presents a simple and exact joint confidence region as well. In all cases, simulation studies show that the proposed approaches are more satisfactory and reliable than previous methods. All proposed approaches are illustrated using a real example.

    Keywords: Coverage probability, generalized confidence interval, generalized p-value, records, Weibull distribution.

    Pages: 3–18

  • Small area estimation of poverty indicators under partitioned area-level time models

    Domingo Morales, Maria Chiara Pagliarella and Renato Salvatore

    Abstract: his paper deals with small area estimation of poverty indicators. Small area estimators of these quantities are derived from partitioned time-dependent area-level linear mixed models. The introduced models are useful for modelling the different behaviour of the target variable by sex or any other dichotomic characteristic. The mean squared errors are estimated by explicit formulas. An application to data from the Spanish Living Conditions Survey is given.

    Keywords: Area-level models, small area estimation, time correlation, poverty indicators.

    Pages: 19–34

  • A new class of Skew-Normal-Cauchy distribution

    Jaime Arrué, Héctor W. Gomez, Hugo S. Salinas and Heleno Bolfarine

    Abstract: In this paper we study a new class of skew-Cauchy distributions inspired on the family extended two-piece skew normal distribution. The new family of distributions encompasses three well known families of distributions, the normal, the two-piece skew-normal and the skew-normal-Cauchy distributions. Some properties of the new distribution are investigated, inference via maximum likelihood estimation is implemented and results of a real data application, which reveal good performance of the new model, are reported.ious methods. All proposed approaches are illustrated using a real example.

    Keywords: Cauchy distribution, kurtosis, maximum likelihood estimation, singular information matrix, skewness, Skew-Normal-Cauchy distribution.

    Pages: 35–50

  • Diagnostic plot for the Identification of high leverage collinearity-influential observations

    Arezoo Bagheri and Habshah Midi

    Abstract: High leverage collinearity influential observations are those high leverage points that change the multicollinearity pattern of a data. It is imperative to identify these points as they are responsible for misleading inferences on the fitting of a regression model. Moreover, identifying these observations may help statistics practitioners to solve the problem of multicollinearity, which is caused by high leverage points. A diagnostic plot is very useful for practitioners to quickly capture abnormalities in a data. In this paper, we propose new diagnostic plots to identify high leverage collinearity influential observations. The merit of our proposed diagnostic plots is confirmed by some well-known examples and Monte Carlo simulations.

    Keywords: Collinearity influential observation, diagnostic robust generalized potential, high lever-age points, multicollinearity.

    Pages: 51–70

  • Discrete Alpha-Skew-Laplace distribution

    S. Shams Harandi and M. H. Alamatsaz

    Abstract: Classical discrete distributions rarely support modelling data on the set of whole integers. In this paper, we shall introduce a flexible discrete distribution on this set, which can, in addition, cover bimodal as well as unimodal data sets. The proposed distribution can also be fitted to positive and negative skewed data. The distribution is indeed a discrete counterpart of the continuous alpha-skew-Laplace distribution recently introduced in the literature. The proposed distribution can also be viewed as a weighted version of the discrete Laplace distribution. Several distributional properties of this class such as cumulative distribution function, moment generating function, moments, modality, infinite divisibility and its truncation are studied. A simulation study is also performed. Finally, a real data set is used to show applicability of the new model comparing to several rival models, such as the discrete normal and Skellam distributions.

    Keywords: Discrete Laplace distribution, discretization, maximum likelihood estimation, uni-bimodality, weighted distribution.

    Pages: 71–84

  • A mathematical programming approach for different scenarios of bilateral bartering

    Stefano Nasini, Jordi Castro and Pau Fonseca

    Abstract: The analysis of markets with indivisible goods and fixed exogenous prices has played an important role in economic models, especially in relation to wage rigidity and unemployment. This paper provides a novel mathematical programming based approach to study pure exchange economies where discrete amounts of commodities are exchanged at fixed prices. Barter processes, consisting in sequences of elementary reallocations of couple of commodities among couples of agents, are formalized as local searches converging to equilibrium allocations. A direct application of the analysed processes in the context of computational economics is provided, along with a Java implementation of the described approaches.

    Keywords: Numerical optimization, combinatorial optimization, microeconomic theory.

    Pages: 85–108

  • A comparison of computational approaches for maximum likelihood estimation of the Dirichlet parameters on high-dimensional data

    Marco Giordan and Ron Wehrens

    Abstract: Likelihood estimates of the Dirichlet distribution parameters can be obtained only through numerical algorithms. Such algorithms can provide estimates outside the correct range for the parameters and/or can require a large amount of iterations to reach convergence. These problems can be aggravated if good starting values are not provided. In this paper we discuss several approaches that can partially avoid these problems providing a good trade-off between efficiency and stability. The performances of these approaches are compared on high-dimensional real and simulated data.

    Keywords: Levenberg-Marquardt algorithm, re-parametrization, starting values, metabolomics data.

    Pages: 109–126

  • The exponentiated discrete Weibull distribution

    Vahid Nekoukhou and Hamid Bidram

    Abstract: In this paper, the exponentiated discrete Weibull distribution is introduced. This new generalization of the discrete Weibull distribution can also be considered as a discrete analogue of the exponentiated Weibull distribution. A special case of this exponentiated discrete Weibull distribution defines a new generalization of the discrete Rayleigh distribution for the first time in the literature. In addition, discrete generalized exponential and geometric distributions are some special sub-models of the new distribution. Here, some basic distributional properties, moments, and order statistics of this new discrete distribution are studied. We will see that the hazard rate function can be in- creasing, decreasing, bathtub, and upside-down bathtub shaped. Estimation of the parameters is illustrated using the maximum likelihood method. The model with a real data set is also examined.

    Keywords: Discrete generalized exponential distribution, exponentiated discrete Weibull distribution, exponentiated Weibull distribution, geometric distribution, infinite divisibility, order statistics, resilience parameter family, stress-strength parameter.

    Pages: 127–146

Volume 38, number 2 (July–December 2014)

Volume 38, number 1 (January–June 2014)

Volume 37, number 2 (July–December 2013)

Volume 37, number 1 (January–June 2013)

Volume 36, number 2 (July–December 2012)

Volume 36, number 1 (January–June 2012)

Volume 35, number 2 (July–December 2011)

Special issue: Privacy in statistical databases. September 2011

Volume 35, number 1 (January–June 2011)

Volume 34, number 2 (July–December 2010)

Volume 34, number 1 (January–June 2010)

Volume 33, number 2 (July–December 2009)

Special issue. 30 years of Qüestiió-SORT (1977–2007) and Centenari del naixement de Joaquim Torrens-Ibern (December 2009)

Volume 33, number 1 (January–June 2009)

Volume 32, number 2 (July–December 2008)

Volume 32, number 1 (January–June 2008)

Volume 31, number 2 (July–December 2007)

Volume 31, number 1 (January–June 2007)

Special issue. Albert Prat in memoriam (April 2006)

Volume 30, number 2 (July–December 2006)

Volume 30, number 1 (January–June 2006)

Volume 29, number 2 (July–December 2005)

Volume 29, number 1 (January–June 2005)

Volume 28, number 2 (July–December 2004)

Volume 28, number 1 (January–June 2004)

Volume 27, number 2 (July–December 2003)

Volume 27, number 1 (January–June 2003)