Showing papers in "Statistica in 2006"
TL;DR: In this paper, Gupta et al. study the family of distributions termed as exponentiated Weibull distribution and compare the behavior of the failure rate with those of the Weibbull and Gamma distributions.
Abstract: In this paper we study the family of distributions termed as exponentiated Weibull distribution. The distribution has three parameters (one scale and two shape) and the Weibull distribution and the exponentiated exponential distribution, discussed by Gupta, et al. (1998), are particular cases of it. The survival function, failure rate and moments of the distributions have been derived using certain special formulas. The behavior of the failure rate has been studied and compared with those of the Weibull and Gamma distributions. The distribution has been fitted to a real life data set and the fit has been found to be very good.
146 citations
TL;DR: The only model with the flexibility, power, and economic and stochastic foundations to accurately fit net and total wealth distributions is the Dagum general model and its particular cases as validated with the case studies of Ireland, U.K., Italy and U.S. as mentioned in this paper.
Abstract: After Pareto developed his Type I model in 1895, a large number of income distribution models have been specified. However, the important issue of wealth distribution called the attention of researchers more than sixty years later. It started with the contributions by Wold and Whittle, and Sargan, both published in 1957. The former authors proposed the Pareto Type I model and the latter the lognormal distribution, but they did not empirically validate them. Afterward, other models were proposed: in 1969 the Pareto Types I and II by Stiglitz; in 1975, the loglogistic by Atkinson and the Pearson Type V by Vaughan. In 1990 and 1994, Dagum developed a general model and his type II as models of wealth distribution. They were validated with real life data from the U.S.A., Canada, Italy and the U.K. In 1999, Dagum further developed his general model of net wealth distribution with support (??,?) which contains, as particular cases, his Types I and II model of income and wealth distributions. This study presents and analyzes the proposed models of wealth distribution and their properties. The only model with the flexibility, power, and economic and stochastic foundations to accurately fit net and total wealth distributions is the Dagum general model and its particular cases as validated with the case studies of Ireland, U.K., Italy and U.S.A.
26 citations
TL;DR: In this article, an IRT model for ordered polytomous variables is considered in order to investigate the item properties and to evaluate the student achievement, and the results highlight the different composition of the items and provide a simple description of the student ability distribution.
Abstract: Recently, the Faculty of Political Science at the University of Bologna has started a program of didactics reorganization for several courses, introducing more than one evaluation test during the learning process. Student assessment before the final examination has the double aim of measuring both the level of student’s ability and the effectiveness of the teaching process, in order to correct it real-time. In such an evaluation system, common to the Anglo-Saxon countries, Item Response Theory (IRT) expresses its effectiveness fully. In this paper, an IRT model for ordered polytomous variables is considered in order to investigate the item properties and to evaluate the student achievement. Particularly, the Graded Response Model (GRM) is taken into account in the analysis of three different written tests of a basic Statistics course. The results highlight the different composition of the items and provide a simple description of the student ability distribution.
20 citations
TL;DR: In this paper, some test procedures for scale parameters of exponential and rectangular distributions involving the median ranked set sampling (MRSS) method are discussed and the necessary tables for the critical regions for the suggested tests are supplied.
Abstract: In this paper, some test procedures for scale parameters of exponential and rectangular distributions involving the median ranked set sampling (MRSS) method are discussed. The necessary tables for the critical regions for the suggested tests are supplied. The power functions of the tests are compared with the power functions of the same tests suggested by Abu-Dayyeh and Muttlak (1996) using ranked set sampling (RSS) data. It is seen that the test procedures using the MRSS data have greater power than those using the RSS data when the sample is drawn from an exponential distribution.
9 citations
TL;DR: In this article, the authors reconstruct the historical trend of the heights of conscripts born in the province of Friuli in the years 1846-90 and identify the problems encountered when using enrolment lists and propose solutions to correct these problems.
Abstract: The aim of this article is to reconstruct the historical trend of heights of conscripts born in the province of Friuli in the years 1846-90. This work is dedicated to identifying the problems encountered when using enrolment lists and to proposing solutions which can, at least in part, correct these problems. Particular interest is posed in evidencing the very high importance of using homogeneous measurements and in introducing some techniques which have allowed us to render statures uniform and therefore also comparable over time. The results obtained bring to light some possible weak points of the series of Italian historical heights which has been used up to date.
7 citations
TL;DR: In this paper, the authors provide an overview of some trend models formulated for global and local estimation based on the assumption that the trend or nonstationary mean of a time series can be approximated closely by simple functions of time over the entire span of the series.
Abstract: In this paper we provide an overview of some trend models formulated for global and local estimation Global trend models are based on the assumption that the trend or nonstationary mean of a time series can be approximated closely by simple functions of time over the entire span of the series The most common representation of deterministic and stochastic trend are introduced In particular, for the former we analyze polynomial and transcendental functions, whereas for the latter we assume that the series from which the trend will be identified follows a homogeneous linear nonstationary stochastic process Recently more attention has been oriented on the analysis of the short term trend, that includes cyclical fluctuations and is referred to as trend-cycle At this regard, we analyze the local polynomial regression predictors developed by Henderson (1916) and LOESS due to Cleveland (1979), which are the most widely applied to estimate the short term local trend of seasonally adjusted economic indicators
6 citations
TL;DR: In this article, the authors delineate the circumstances and the basic theoretical steps which led, about thirty years ago, to the derivation of the Dagum income distribution as the equilibrium distribution of a diffusion process.
Abstract: The present notes delineates the circumstances and the basic theoretical steps which led, about thirty years ago, to the derivation of the Dagum income distribution as the equilibrium distribution of a diffusion process. Most of theoretical issues of this note deal with the derivation of the stable solution for the forward Kolmogorov equation. Such a derivation has socio-economic fundaments from the contributions of Sylos Labini on social stratification.
5 citations
TL;DR: In this paper, the complete expectation of life for a person and the actuarial present value of continuous life annuities are defined by integrals, and closed form integrations are hereafter provided by means of the incomplete Gamma function.
Abstract: The complete expectation-of-life for a person and the actuarial present value of continuous life annuities are defined by integrals. In all of them at least one of the factors is a survival function value ratio. If de Moivre’s law of mortality is chosen, such integrals can easily be evaluated; but if the Makeham survival function is adopted, they are used to be calculated numerically. For the above actuarial figures, closed form integrations are hereafter provided by means of the incomplete Gamma function.
5 citations
TL;DR: In this article, the estimation of human capital distribution is obtained by means of Dagum model, which refers to Italian households human capital, measured by resorting to Wold's latent variables method, on the basis of micro data provided by the Bank of Italy's survey of household income and wealth.
Abstract: In this paper the estimation of human capital distribution is obtained by means of Dagum model. The analysis refers to Italian households human capital, measured by resorting to Wold’s latent variables method, on the basis of micro data provided by the Bank of Italy’s survey of household income and wealth. The Dagum model allows both to achieve parameters with a specific economic significance and to reconcile economic theory with empirical evidence.
4 citations
TL;DR: A hierarchical spatio-temporal Bayesian model is proposed for the calibration of measurements recorded using non-reference samplers, by borrowing strength from non co-located reference sampler measurements.
Abstract: PM10 monitoring networks are equipped with heterogeneous samplers. Some of these samplers are known to underestimate true levels of concentrations (non-reference samplers). In this paper we propose a hierarchical spatio-temporal Bayesian model for the calibration of measurements recorded using non-reference samplers, by borrowing strength from non co-located reference sampler measurements.
4 citations
TL;DR: Mapping the electronic database containing all relevant data about the students, named “datawarehouse”, for three academic years aims to infer on the dynamics and structural mechanisms that lead the evolution and topology of this complex system.
Abstract: The movements of students between the faculties of the University of Bologna represent a complex evolving network. By mapping the electronic database containing all relevant data about the students, named “datawarehouse”, for three academic years (2004-2007), we aim to infer on the dynamics and the structural mechanisms that lead the evolution and topology of this complex system. Empirical measurements allow us to discover the topological characteristics of the network at a given moment, as well as their evolution in time. The results highlight stable ‘attraction’ and ‘escape’ nodes within the University network, and provide a simple description of the student movements and preferences.
TL;DR: In this paper, an improved method for the estimation of household Human Capital (HC) as a Latent Variable (LV) by means of formative and reflective indicators in agreement with the accepted economic definition of HC is introduced.
Abstract: Dagum and Slottje (2000) estimated household Human Capital (HC) as a Latent Variable (LV) proposing its monetary estimation by means of an actuarial approach. This paper introduces an improved method for the estimation of household HC as LV by means of formative and reflective indicators in agreement with the accepted economic definition of HC. The monetary HC distribution, estimated for Italian (2000) and US (2004) household, is used in a recursive causal model to explore the role of HC in macroeconomy.
TL;DR: In this article, the authors study the properties of a family of index, called CI, proposed by Civardi, Zavarrone (2003) in order to evaluate the teaching quality in university disciplines and find that all effective distributions, varying N and k, are symmetric with mean, mode and median equal to zero.
Abstract: In this paper we study the properties of a family of index, called CI These indices have been proposed by Civardi, Zavarrone (2003) in order to evaluate the teaching quality in university disciplines The most frequently used scales offer four or five points and the first two (or the last two) points on both scales are associated with negative evaluations and the last two (or the first two) are associated with symmetric positive evaluations The empirical distribution of responses represents the starting point to compute the CI indices Each index assumes values lying between –100 (in the case of maximum negative evaluation) to +100 (in the case of an evaluation of absolute excellence) and is obtained as the algebraic sum of two indices The first expresses the score obtained in the semi-plane of positive evaluations while the second represents the score obtained in the semi-plane of negative evaluations The CI index is characterized by the choice of the parameter of importance level k (0?k?1) on the degree of importance the “investigator/decision maker” wants to assign to the quota of very positive opinions and of the very negative ones The construction of the universe of response models of N respondents (with 10?N?105) and, for each distribution, of the eleven CI indices (k=0, 01, , 09, 1)) allow to study the properties of effective distributions of the indices The results highlight that all effective distributions, varying N and k, are symmetric with mean, mode and median equal to zero The square mean error assumes values from 53 (when N=10 and k=0) to 31 The possibility of approximating CI distribution with a normal one offers interesting developments in an inferential framework
TL;DR: In this article, the limiting distributions for sequences of central terms under power nonrandom normalization are obtained and the classes of the limit types having domain of L- attraction are investigated.
Abstract: In this paper the limiting distributions for sequences of central terms under power nonrandom normalization are obtained. The classes of the limit types having domain of L- attraction are investigated.
TL;DR: In this paper, the authors consider two time series of categorical data as a bivariate Markov chain and show that the proposed conditions are equivalent to the hypothesis of null coefficients in some parametric models for joint transition probabilities.
Abstract: In this work we consider two time series of categorical data as a bivariate Markov chain. The markovianity assumption allows us to simplify some conditional independencies introduced in order to describe if the knowledge of past or present realizations of one of the two categorical variables can provide some additional information to forecast the current realization of the other. The three simple conditions introduced here, though referring only to the recent realizations of the two variables, imply the more general conditions defined by all of the past realizations. Moreover, we show that the proposed conditions are equivalent to the hypothesis of null coefficients in some parametric models for joint transition probabilities. Finally, we represent these conditions in terms of missing edges in chain graphs.
TL;DR: In this article, an analysis of the technical efficiency in the formation of 2,236 graduates in 1998 in the University of Florence, that is, in the university human capital formation, is performed, by modelling the production process as one in which the student produces himself as a graduate.
Abstract: In this paper, an analysis of the technical efficiency in the formation of 2,236 graduates in 1998 in the University of Florence, that is, in the university human capital formation, is performed, by modelling the production process as one in which the student produces himself as a graduate. The tool utilized is the DEA methodology, under the hypothesis of variable returns to scale. The production factors are represented by a set of human and capital resources provided by the faculties, along with individual factors represented by secondary school diploma score and by the length of university study. The analysis is conducted both for the overall graduates, and at a faculty level, in order to emphasize the contribution provided by the latter to efficiency. There is evidence that the students graduated with an average efficiency greater than 90% and therefore with an unexploited productive capacity lower than 10%. At a faculty level, Formation Science appears to be the most efficient, whereas Economics is the less efficient one. By and large, the contribution to efficiency provided by faculties is greater than that brought by students individual characteristics.
TL;DR: In this paper, the authors combine the empirical likelihood for the mean functional with jackknife pseudo-values obtained from the Mann-Witney two-sample statistic, leading to a pseudo-likelihood L(p) for the area p0 under the ROC curve.
Abstract: Following an idea by Jing et al. (2005), this paper combines the empirical likelihood for the mean functional with jackknife pseudo-values obtained from the Mann-Witney two-sample statistic. This leads to a pseudo-likelihood L(p) for the area p0 under the ROC curve. A Wilks-type theorem is proved, so that L(p) can be used in a standard way to obtain approximate confidence intervals for p0. Some simulation results are given, in order to show the usefulness of the proposed method.
TL;DR: In this paper, a design of experiments technique is used to fit a model for TMF lives in hot forging dies, where the variation of some hundreds of °C is operated in a few seconds and thermal gradient is present.
Abstract: Investigation of thermo-mechanical fatigue (TMF) phenomena usually involves complex experimentation and long testing runs, as well as difficulties in specifying and fitting appropriate models. Moreover, the experimental techniques usually consider temperature in the specimen to be constant, or slowly varying, often with a uniform distribution of temperature in the cross section of the specimen but it is not a plausible assumption. Aimed at extending the investigation to hot forging dies, where the variation of some hundreds of °C is operated in a few seconds and thermal gradient (some tens of °C per mm) is present, the experimental configuration become more complex. The present paper focuses on a recently proposed experiment for a TMF investigation of hot forging dies where Design of Experiments techniques are used to fit a model for TMF lives. This study allows to detect which factors are more important in affecting the TMF, to “describe” the relationship between TMF and these factors and to predict TMF lives. Experimental data are analyzed using Response Surface Modelling (RSM) in order to fit an empirical linear model.
TL;DR: This paper introduces a structure learning procedure, that it is called the qp-procedure, based on limited-order partial correlations, which is implemented in a freely available package for the statistical software R.
Abstract: Learning of large-scale networks of interactions from microarray data is an important and challenging problem in bioinformatics. A widely used approach is to assume that the available data constitute a random sample from a multivariate distribution belonging to a Gaussian graphical model. As a consequence, the prime objects of inference are full-order partial correlations which are partial correlations between two variables given the remaining ones. In the context of microarray data the number of variables exceeds the sample size and this precludes the application of traditional structure learning procedures because a sampling version of full-order partial correlations does not exist. In this paper we introduce a structure learning procedure, that we call the qp-procedure, based on limited-order partial correlations. The procedure is implemented in a freely available package for the statistical software R.
TL;DR: In this article, some procedures for testing hypotheses about the scale parameters of the uniform and exponential distributions using selected ranked set sampling (SRSS) data are described, and the critical regions and the power function of the test procedures are computed using numerical integration.
Abstract: Some procedures for testing hypotheses about the scale parameters of the uniform and exponential distributions using selected ranked set sampling (SRSS) data are described in this paper. Using numerical integration the critical regions and the power function of the test procedures are computed and the necessary tables for the critical regions are supplied.
Posted Content•
TL;DR: In this article, the authors investigated the impact of the realizazione of a mutabile dipenda on the realisation of a catena di Markov bivariata.
Abstract: Per una serie storica categoriale bivariata, l’osservazione al tempo t e una coppia di modalita che indica come si manifestano due mutabili At e Bt, aventi rispettivamente a e b categorie E’ lecito in questo contesto domandarsi se sapere che nell’istante d’osservazione una mutabile ha assunto una certa modalita puo suggerire quale categoria sara piu probabile per l’altra risposta nell’istante seguente; oppure chiedersi se la realizzazione di una mutabile dipenda o meno da come si manifesta l’altra nel medesimo istante dato il passato di entrambe; o ancora se conoscere la modalita di una mutabile nell’istante corrente renda del tutto ininfluente il suo passato quando l’interesse e rivolto al presente dell’altra risposta Tali interrogativi mostrano le potenzialita dell’ottica dinamica in cui la generica realizzazione di ciascuna delle due serie categoriali, e considerata come risultante dell’effetto del passato della medesima mutabile, e del passato e presente dell’altra Per stabilire se la storia passata effettivamente influisca sul presente, e se ci sia dipendenza tra realizzazioni contemporanee bisognera verificare delle condizioni descritte in seguito utilizzando il concetto di indipendenza condizionale Le condizioni d’indipendenza (introdotte nel paragrafo 2) includono tutte le possibili realizzazioni dei due processi fino all’istante attuale di osservazione Nel paragrafo 3, sotto l’ipotesi che le due serie formino una catena di Markov bivariata, per semplicita del primo ordine, si mostra che le precedenti condizioni si semplificano in modo da coinvolgere soltanto le realizzazioni piu recenti delle due mutabili Nel quarto paragrafo, le indipendenze proposte sono ricondotte ad ipotesi lineari sui parametri di un’opportuna parametrizzazione con cui si specifica come le probabilita di transizione di una catena di Markov bivariata dipendano da covariate e dalla storia passata delle due risposte Grafi catena (nel paragrafo 5) illustreranno come l’assenza di connessioni tra nodi descriva le indipendenze condizionali introdotte ed un esempio nel paragrafo 6 servira ad evidenziare l’utilita della metodologia proposta
TL;DR: Singh and Dey as mentioned in this paper constructed a class of simple partially efficiency balanced row-Column designs (SPEB RC-designs) by replacing the diagonal treatments of a 2v x 2v standard cyclic Latin square by a new treatment 2v+1.
Abstract: A class of Row-Column designs in two sets of treatments having different replications has been constructed by replacing the diagonal treatments of a 2v x 2v standard cyclic Latin Square by a new treatment ‘2v+1’. The designs so obtained have been identified as Simple partially efficiency balanced Row-Column designs (SPEB RC-designs) (Singh and Dey, 1978; Pal, 1980).
TL;DR: In this article, an estimator of the parameters of interest, x, so that a Wald-type test statistic can be used for testing H 0 is presented, which is obtained through the maximization of a modified (penalized) log-likelihood function.
Abstract: We face an indeterminate parameters problem when there are two sets of parameters, x and g, say, such that the null hypothesis H0:x=x0 makes the likelihood independent of g. A consequence of indeterminacy is the singularity of the information matrix. For this problem the standard results, such as the asymptotic chi-squared distribution of the Wald test statistic, are generally false. In the paper we propose an estimator of the parameters of interest, x, so that a Wald-type test statistic can be used for testing H0. Such an estimator is obtained through the maximization of a modified (penalized) log-likelihood function. We show that a solution to the (penalized) likelihood equation is consistent and asymptotically normally distributed with variance-covariance matrix approximated by the Moore-Penrose pseudoinverse of the information matrix. These properties allow one to construct a Wald-type test statistic useful for inferential purposes.