Journal of Data Science

Abstract: In this paper, we reconsider the two-factor stochastic mortality model introduced by Cairns, Blake and Dowd (2006) (CBD). The error terms in the CBD model are assumed to form a two-dimensional random walk. We first use the Doornik and Hansen (2008) multivariate normality test to show that the underlying normality assumption does not hold for the considered data set. Ainou (2011) proposed independent univariate normal inverse Gaussian L´evy processes to model the error terms in the CBD model. We generalize this idea by introducing a possible dependency between the 2-dimensional random variables, using a bivariate Generalized Hyperbolic distribution. We propose four non-Gaussian, fat-tailed distributions: Stu dent’s t, normal inverse Gaussian, hyperbolic and generalized hyperbolic distributions. Our empirical analysis shows some preferences for using the new suggested model, based on Akaike’s information criterion, the Bayesian information criterion and likelihood ratio test, as our in-sample model selec tion criteria, as well as mean absolute percentage error for our out-of-sample projection errors.

Abstract: The University of Michigan’s Consumer Sentiment Index has pre occupied politicians, journalists, and Wall Street for decades (Uchitelle, 2002). This American economic indicator is now co-published with Thomson Reuters in London. The international reach of this index cries out for an other look at George Katona’s consumer sentiment construct as a predictor of consumer demand. Regressions from the British Household Panel Sur vey (BHPS) show that consumer sentiment is ineffectual in predicting micro variation in discretionary spending between consumers, within consumers over time, or between and within consumers overall. Moreover, consumer sentiment bears no relationship whatsoever to national consumer demand over annual BHPS surveys from 1997 to 2008. In contrast, an indicator of economic anxiety accounts for all three types of variation in micro demand, as well as variation in macro demand over time.

Abstract: The problem of variable selection is fundamental to statistical modelling in diverse fields of sciences. In this paper, we study in particular the problem of selecting important variables in regression problems in the case where observations and labels of a real-world dataset are available. At first, we examine the performance of several existing statistical methods for analyzing a real large trauma dataset which consists of 7000 observations and 70 factors, that include demographic, transport and intrahospital data. The statistical methods employed in this work are the nonconcave penalized likelihood methods (SCAD, LASSO, and Hard), the generalized linear logis tic regression, and the best subset variable selection (with AIC and BIC), used to detect possible risk factors of death. Supersaturated designs (SSDs) are a large class of factorial designs which can be used for screening out the important factors from a large set of potentially active variables. This paper presents a new variable selection approach inspired by supersaturated designs given a dataset of observations. The merits and the effectiveness of this approach for identifying important variables in observational studies are evaluated by considering several two-levels supersaturated designs, and a variety of different statistical models with respect to the combinations of factors and the number of observations. The derived results are encour aging since the alternative approach using supersaturated designs provided specific information that are logical and consistent with the medical experi ence, which may also assist as guidelines for trauma management.

Abstract: The Weibull distribution is the most important distribution for problems in reliability. We study some mathematical properties of the new wider Weibull-G family of distributions. Some special models in the new family are discussed. The properties derived hold to any distribution in this family. We obtain general explicit expressions for the quantile function, or dinary and incomplete moments, generating function and order statistics. We discuss the estimation of the model parameters by maximum likelihood and illustrate the potentiality of the extended family with two applications to real data.

Abstract: Mixture of Weibull distributions has wide application in modeling of heterogeneous data sets. The parameter estimation is one of the most important problems related to mixture of Weibull distributions. In this pa per, we propose a L-moment estimation method for mixture of two Weibull distributions. The proposed method is compared with maximum likelihood estimation (MLE) method according to the bias, the mean absolute error, the mean total error and completion time of the algorithm (time) by sim ulation study. Also, applications to real data sets are given to show the flexibility and potentiality of the proposed estimation method. The com parison shows that, the proposed method is better than MLE method.

Abstract: Chen, Bunce and Jiang [In: Proceedings of the International Con ference on Computational Intelligence and Software Engineering, pp. 1-4] claim to have proposed a new extreme value distribution. But the formulas given for the distribution do not form a valid probability distribution. Here, we correct their formulas to form a valid probability distribution. For this valid distribution, we provide a comprehensive treatment of mathematical properties, estimate parameters by the method of maximum likelihood and provide the observed information matrix. The flexibility of the distribution is illustrated using a real data set.

Abstract: In this paper, we propose a flexible cure rate survival model by as suming that the number of competing causes of the event of interest follows the negative binomial distribution and the time to event follows a generalized gamma distribution. We define the negative binomial-generalized gamma distribution, which can be used to model survival data. The new model in cludes as special cases some of the well-known cure rate models discussed in the literature. We consider a frequentist analysis and nonparametric boot strap for parameter estimation of a negative binomial-generalized gamma regression model with cure rate. Then, we derive the appropriate matri ces for assessing local influence on the parameter estimates under different perturbation schemes and present some ways to perform global influence analysis. Finally, we analyze a real data set from the medical area.

Abstract: The study of pattern of female child birth is one of the most crucial area of human demography because it plays very important role in the building of a nation. In the present study, an attempt has been made to work-out the pattern of female child births among females belongs to different subdomains of population through the probability model and the parameters involved in the probability model under consideration has also been estimated. The suggested model, for illustration has been applied to an observed set of data taken from NFHS-III (2005-06) for the seven North East states of India known as Seven Sisters.

Abstract: The present paper deals with the maximum likelihood and Bayes estimation procedure for the shape and scale parameter of Poisson-exponential distribution for complete sample. Bayes estimators under symmetric and asymmetric loss function are obtained using Markov Chain Monte Carlo (MCMC) technique. Performances of the proposed Bayes estimators have been studied and compared with their maximum likelihood estimators on the basis of Monte Carlo study of simulated samples in terms of their risks. The methodology is also illustrated on a real data set.

Abstract: The assessment of modality or “bumps” in distributions is of in terest to scientists in many areas. We compare the performance of four statistical methods to test for departures from unimodality in simulations, and further illustrate the four methods using well-known ecological datasets on body mass published by Holling in 1992 to illustrate their advantages and disadvantages. Silverman’s kernel density method was found to be very conservative. The excess mass test and a Bayesian mixture model approach showed agreement among the data sets, whereas Hall and York’s test pro vided strong evidence for the existence of two or more modes in all data sets. The Bayesian mixture model also provided a way to quantify the un certainty associated with the number of modes. This work demonstrates the inherent richness of animal body mass distributions but also the difficulties for characterizing it, and ultimately understanding the processes underlying them.