Last year's top ten most cited papers
Top ten most cited papers in 2019 according to Web of Science (WOS)
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.
Vol 39 (2) 2015
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.
Vol 39 (2) 2015
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.
Vol 39 (1) 2015
The normal distribution in some constrained sample spaces
Glòria Mateu-Figueras, Vera Pawlowsky-Glahn and Juan-José Egozcue
Abstract: Phenomena with a constrained sample space appear frequently in practice. This is the case,for example, with strictly positive data, or with compositional data, such as percentages orproportions. If the natural measure of difference is not theabsolute one, simple algebraicproperties show that it is more convenient to work with a geometry different from the usualEuclidean geometry in real space, and with a measure different from the usual Lebesguemeasure, leading to alternative models that better fit the phenomenon under study. The generalapproach is presented and illustrated using the normal distribution, both on the positive real lineand on theD-part simplex. The original ideas of McAlister in his introduction to the lognormaldistribution in 1879, are recovered and updated.
Keywords: Additive logistic normal distribution, Aitchison measure, Lebesgue measure, lognor-mal distribution, orthonormal basis, simplex.
Vol 37 (1) 2013
Decision making techniques with similarity measures and OWA operators
José M. Merigó and Anna M. Gil-Lafuente
Abstract: We analyse the use of the ordered weighted average (OWA) in decision-making giving specialattention to business and economic decision-making problems. We present several aggregationtechniques that are very useful for decision-making such asthe Hamming distance, the adequacycoefficient and the index of maximum and minimum level. We suggest a new approach by usingimmediate weights, that is, by using the weighted average and the OWA operator in the sameformulation. We further generalize them by using generalized and quasi-arithmetic means. Wealso analyse the applicability of the OWA operator in business and economics and we see that wecan use it instead of the weighted average. We end the paper with an application in a businessmulti-person decision-making problem regarding production management.
Keywords: Decision-making, OWA operator, similarity measure, Hamming distance, productionmanagement.
Vol 36 (1) 2012
Estimation in the Birnbaum-Saunders distribution based on scale-mixture of normals and the EM-algorithm
Narayanaswamy Balakrishnan, Víctor Leiva, Antonio Sanhueza and Filidor Vilca
Abstract: Scale mixtures of normal (SMN) distributions are used for modeling symmetric data. Membersof this family have appealing properties such as robust estimates, easy number generation, andefficient computation of the ML estimates via the EM-algorithm. The Birnbaum-Saunders (BS)distribution is a positively skewed model that is related tothe normal distribution and has receivedconsiderable attention. We introduce a type of BS distributions based on SMN models, producea lifetime analysis, develop the EM-algorithm for ML estimation of parameters, and illustrate theobtained results with real data showing the robustness of the estimation procedure.
Keywords: Birnbaum-Saunders distribution, EM-algorithm, kurtosis, maximum likelihood methods,robust estimation, scale mixtures of normal distribution.
Vol 33 (2) 2009
Stress-strength reliability of Weibull distribution based on progressively censored samples
Akbar Asgharzadeh, Reza Valiollahi, and Mohammad Z. Raqab
Abstract: Based on progressively Type-II censored samples, this paper deals with inference for the stress-strength reliabilityR=P(Y<X) whenXandYare two independent Weibull distributions withdifferent scale parameters, but having the same shape parameter. The maximum likelihood esti-mator, and the approximate maximum likelihood estimator ofRare obtained. Different confidenceintervals are presented. The Bayes estimator ofRand the corresponding credible interval usingthe Gibbs sampling technique are also proposed. Further, weconsider the estimation ofRwhenthe same shape parameter is known. The results for exponential and Rayleigh distributions canbe obtained as special cases with different scale parameters. Analysis of a real data set as well aMonte Carlo simulation have been presented for illustrative purposes.
Keywords: Maximum likelihood estimator, Approximate maximum likelihood estimator, Bootstrapconfidence interval, Bayesian estimation, Metropolis-Hasting method, Progressive Type-II censorin.
Vol 35 (2) 2011
Construction of multivariate distributions: a review of some recent results
José María Sarabia and Emilio Gómez-Déniz
Abstract: The construction of multivariate distributions is an active field of research in theoretical and appliedstatistics. In this paper some recent developments in this field are reviewed. Specifically, we studyand review the following set of methods: (a) Construction of multivariate distributions based on orderstatistics, (b) Methods based on mixtures, (c) Conditionally specified distributions, (d) Multivariate skewdistributions, (e) Distributions based on the method of the variables in common and (f) Other methods,which include multivariate weighted distributions, vines and multivariate Zipf distributions.
Keywords: Order statistics, Rosenblatt transformation, mixture distributions, conditionally specified dis-tributions, skew distributions, variables in common, multivariate weighted distributions, vines, mul-tivariate Zipf distributions, associated random variables.
Vol 32 (1) 2008
The new class of Kummer beta generalized distributions
Rodrigo R. Pescim, Gauss M. Cordeiro, Clarice G. B. Demétrio, Edwin M. M. Ortega and Saralees Nadarajah
Abstract: Ng and Kotz (1995) introduced a distribution that provides greater flexibility to extremes. We defineand study a new class of distributions called the Kummer betageneralized family to extend thenormal, 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 familycan 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 functionof the order statistics, mean absolute deviations and entropies. We use maximum likelihoodestimation to fit the distributions in the new class and illustrate its potentiality with an applicationto a real data set.
Keywords: Generalized distribution, Kummer beta distribution, likelihood ratio test, moment, orderstatistic, Weibull distribution.
Vol 36 (2) 2012
On developing ridge regression parameters: a graphical investigation
Gisela Muniz, B. M. Golam Kibria, Kristofer Mansson and Ghazi Shukur
Abstract: In this paper we review some existing and propose some new estimators for estimating the ridgeparameter. All in all 19 different estimators have been studied. The investigation has been carriedout using Monte Carlo simulations. A large number of different models have been investigatedwhere the variance of the random error, the number of variables included in the model, thecorrelations among the explanatory variables, the sample size and the unknown coefficient vectorwere varied. For each model we have performed 2000 replications and presented the results bothin term of figures and tables. Based on the simulation study, we found that increasing the numberof correlated variable, the variance of the random error andincreasing the correlation betweenthe independent variables have negative effect on the mean squared error. When the sample sizeincreases the mean squared error decreases even when the correlation between the independentvariables and the variance of the random error are large. In all situations, the proposed estimatorshave smaller mean squared error than the ordinary least squares and other existing estimators.
Keywords: Linear model, LSE, MSE, Monte Carlo simulations, multicollinearity, ridge regression.
Vol 36 (2) 2012