International Journal of Statistics and Probability
http://ccsenet.org/journal/index.php/ijsp
<em><strong>International Journal of Statistics and Probability</strong> </em>(ISSN: 1927-7032; E-ISSN: 1927-7040) is an open-access, international, double-blind peer-reviewed journal published by the Canadian Center of Science and Education. This journal, published <strong>quarterly</strong> (February, May, August and November) in both<strong> print and online versions</strong>, keeps readers up-to-date with the latest developments in all areas of statistics and probability.<img src="/journal/public/site/images/ijsp/ijsp.jpg" alt="ijsp" hspace="20" vspace="20" width="201" height="264" align="right" /><p><strong>The scopes of the journal </strong>include, but are not limited to, the following topics: computational statistics, design of experiments, sample survey, statistical modelling, statistical theory, probability theory.</p><p>This journal accepts article submissions<strong> <a href="/journal/index.php/ijsp/information/authors">online</a> or by <a href="mailto:ijsp@ccsenet.org">e-mail</a> </strong>(ijsp@ccsenet.org).</p><p><strong><strong>ABSTRACTING AND INDEXING:</strong></strong></p><ul><li><strong>DOAJ</strong></li><li><strong>EBSCOhost</strong></li><li>Google Scholar</li><li>JournalTOCs</li><li>Library and Archives Canada</li><li>LOCKSS</li><li>PKP Open Archives Harvester</li><li><strong>ProQuest</strong></li><li>SHERPA/RoMEO</li><li>Standard Periodical Directory</li></ul>Canadian Center of Science and Educationen-USInternational Journal of Statistics and Probability1927-7032<p>Submission of an article implies that the work described has not been published previously (except in the form of an abstract or as part of a published lecture or academic thesis), that it is not under consideration for publication elsewhere, that its publication is approved by all authors and tacitly or explicitly by the responsible authorities where the work was carried out, and that, if accepted, will not be published elsewhere in the same form, in English or in any other language, without the written consent of the Publisher. The Editors reserve the right to edit or otherwise alter all contributions, but authors will receive proofs for approval before publication.</p><p><br />Copyrights for articles published in CCSE journals are retained by the authors, with first publication rights granted to the journal. The journal/publisher is not responsible for subsequent uses of the work. It is the author's responsibility to bring an infringement action if so desired by the author.</p>Model Selection for Poisson Regression via Association Rules Analysis
http://ccsenet.org/journal/index.php/ijsp/article/view/46231
<p class="abstract">This study integrates association rules analysis, a methodology for selecting potential interactions, with Poisson regression modeling. Though typically ignored in conventional Poisson regression, interactions are very common in practice. However, selecting a Poisson regression model when many main effects and interactions are involved is problematic. In this study, we develop a model selection framework to address this problem. Specifically, we focus on building an optimal Poisson regression model by (1) discretizing the response and quantitative attributes into levels; (2) exploring via association rules analysis combinations of input variables that have a significant impact on response; (3) selecting potential (low- and high-order) interactions; (4) converting these potential interactions into new variables; and (5) selecting variables from all the input variables and the newly created variables (interactions) to build the optimal Poisson regression model. Our model selection procedure is the first approach to enable a global search for potential interactions and the first to establish the optimal combination of main effects and interaction effects in the Poisson regression model. A real-life example is given for illustration. It is shown that the proposed method finds the optimal model including important interactions that cannot be found by other existing methods.</p>Pannapa ChangpetchDennis K. J. Lin2015-03-112015-03-114A Bayesian Mixture Model Accounting for Zeros and Negatives in the Loss Triangle
http://ccsenet.org/journal/index.php/ijsp/article/view/46233
In insurance loss reserving, a large portion of zeros are expected at the later development periods of an incremental loss triangle. Negative losses occur frequently in the incremental loss triangle due to actuarial practices such as subrogation and salvation. The nature of the distributions assumed by most stochastic models, such as the lognormal and over-dispersed Poisson distributions, brings restrictions on the zeros and negatives appearing in the loss triangle. In this paper, we propose a Bayesian mixture model for stochastic reserving under the situation where there are both zeros and negatives in the incremental loss triangle. A multinomial regression model will be applied to model the sign of the loss data, while the lognormal distribution is assumed for the loss magnitudes of negatives and positives. Bayesian generalized linear models will be fitted for both the mixture and magnitude models. The model will be implemented using the Markov chain Monte Carlo (MCMC) techniques in BUGS. Our model provides a realistic tool for stochastic reserving in the cases of zeros and negatives.Michelle XiaDavid P. M. Scollnik2015-03-112015-03-114On Some Properties of the Reversed Variance Residual Lifetime
http://ccsenet.org/journal/index.php/ijsp/article/view/43232
In this paper, we give an overview of recent results in the concept of reversed residual lifetime. We focus on properties of the reversed variance residual lifetime (RVR) and study the interrelations among reversed residual lifetime classes. We mention the most important results in the literature that are related to the RFR function for both continuous and discrete life distributions. We give properties of the reversed mean residual lifetime (RMR) and the RVR functions. Reversed entropy is briefly discussed. We study the relationships among the reversed classes.Bander Al-ZahraniMashail Al-Sobhi2015-03-202015-03-204Estimation of P(Y < X) for a Two-parameter Bathtub Shaped Failure Rate Distribution
http://ccsenet.org/journal/index.php/ijsp/article/view/46723
This paper deals with the estimation of reliability R = P[Y < X] when X and Y are two independent random variables with atwo-parameter bathtub shaped failure rate distribution with the samesecond shape parameter. Likelihood and Bayesian methods are proposedto make inferences about R. We obtain the likelihood interval andasymptotic confidence interval for R, and we consider Bayesianpoint estimates of R under both absolute and squared error loss,using either gamma or uniform priors for the three unknown modelparameters. An equal tail Bayesian credible interval for R isinvestigated. Analysis of a real data set is presented forillustrative purposes, and Monte Carlo simulations are performed tocompare: (1) the performance of Bayes estimates under two differentloss functions; and (2) the maximum likelihood and Bayesian methods.Ammar M. SarhanBruce SmithDavid C. Hamilton2015-03-252015-03-254Nonparallel Regressions with Indicator Variables
http://ccsenet.org/journal/index.php/ijsp/article/view/45155
A multiple linear regression model which includes 0/1 variables to indicatemembership in a group is a convenient way to model parallel regression surfaces.Building upon this, an extended model which includes predictor variables thatare the product of the indicator and other variables willcoincide with separate regressions for each group using only the other predictors.The algebraic basis for this concurrence is demonstrated.Least squares estimation is presumed.Examples with two groups and with four groups are presented.Timothy G. Gregoire2015-03-262015-03-264Quantile Plots of the Prediction Variance for Partially Replicated Central Composite Design
http://ccsenet.org/journal/index.php/ijsp/article/view/43972
<p>Sometimes, it is not feasible to fully replicate the experimental units. When this happen, there is need for optimal replication of the experimental units to avoid bias. The prediction variance of two variations of the partially replicated central composite design (replicated cube plus one star and one cube plus replicated star) are compared using the quantile plots. These plots provide information about the prediction variance distribution on a sphere for comprehensive evaluation of the quality of the prediction variance. For face-centred \( ( \alpha = 1) \) and rotatable \( ( \alpha =F^ \frac {1} {4} ) \) central composite designs, the prediction variance of the one cube plus replicated star perform better than the replicated cube plus one star. Unlike the replicated cube plus one star, the quantile plots of the scaled prediction variance of the one cube plus replicated star depict near rotatability.</p>Ngozi C. Umelo-IbemereHarrison O. Amuji2015-03-302015-03-304Inequalities and Approximations of Weighted Distributions by Lindley Reliability Measures, and the Lindley-Cox Model with Applications
http://ccsenet.org/journal/index.php/ijsp/article/view/44836
In this note, stochastic comparisons and results for weighted and Lindley models are presented. Approximation of weighted distributions via Lindley distribution in the class of increasing failure rate (IFR) and decreasing failure rate (DFR) weighted distributions with monotone weight functions are obtained including approximations via the length-biased Lindley distribution. Some useful bounds and moment-type inequality for weighted life distributions and applications are presented. Incorporation of covariates into Lindley model is considered and an application to illustrate the usefulness and applicability of the proposed Lindley-Cox model is given.Broderick O. OluyedeMacaulay OkwuokenyeKarl E. Peace2015-03-302015-03-304Comparison of Two Means of Two Log-Normal Distributions When Data is Singly Censored
http://ccsenet.org/journal/index.php/ijsp/article/view/47291
It is common in environmental and biomedical data analysis to dealwith censored data that are log-normally distributed. This paperis concerned with the statistical analysis for comparing the meansof two independent log-normal distributions from censored datawith a single detection limit. The method of maximum likelihoodwill be used to obtain closed form estimates for populationparameters under different hypotheses. A test procedure forcomparing the means of two independent log-normal populations inthe presence of censored data is also introduced and evaluated.Asymptotic chi-square test is used in the proposed test procedure.Worked example is given illustrating the use of the methodsprovided utilizing a computer program written in the R language.A simulation study was performed to examine the power of the proposed test procedure introduced in this article.Abou El-Makarim A. Aboueissa2015-04-072015-04-074Minimal Generalized Extreme Value Distribution and Its Application in Modeling of Minimum Temperature
http://ccsenet.org/journal/index.php/ijsp/article/view/47805
Distribution of maximum or minimum values (extreme values) of a data set is especially used in natural phenomena including flow discharge, temperature, wind speeds, precipitation and it is also used in many other applied sciences such as reliability studies and analysis of environmental extreme events. So if we can explain the extremes behavior via statistical formulas, we can estimate their behavior in the future. This article is devoted to study extreme values of minimum temperature in Tabriz using minimal generalized extreme value distribution, which all minima of a data set are modeled using it. In this article, we apply four methods to estimate distribution parameters including maximum likelihood estimation, probability weighted moments, elemental percentile and quantile least squares then compare estimates by average scaled absolute error criterion. We also obtain quantiles estimates and confidence intervals and finally perform goodness of fit tests.Farnoosh AshooriMalihe EbrahimpourAtena GharibAbolghasem Bozorgnia2015-04-212015-04-214Comparative Study of the Quick Convergent Inflow Algorithm (QCIA) and the Modified Quick Convergent Inflow Algorithm (MQCIA)
http://ccsenet.org/journal/index.php/ijsp/article/view/46244
<p>The performance of two line search algorithms, the Quick Convergent Inflow Algorithm and the Modified Quick Convergent Inflow Algorithm, used in locating the optimizers of response functions is studied. The methodology requires the use of the same starting experimental design. The indicator variables are the number of iterations and the optimal point reached at each iteration. The Modified Quick Convergent Inflow Algorithm seems to perform generally better than the Quick Convergent Inflow Algorithm in the sense that solutions obtained are much closer to the exact solutions than those obtained using the Quick Convergent Inflow Algorithm. As a consequence to the study, a new algorithm is developed for solving Linear Programming problems. The algorithm iteratively eliminates from an N-sized starting design a point that contributes less to the process as measured by the predictive variances at the design points. The design size is immediately recoverd by adding to the resulting N-1 sized design a design point from the candidate set that optimizes performance. The new algorithm offers approximate solutions to Linear Programming problems as demonstrated with some numerical illustrations.</p><p> </p>M. P. IwunduI. E. Ndiyo2015-04-212015-04-214Characterizations of the Weibull-X and Burr XII Negative Binomial Families of Distributions
http://ccsenet.org/journal/index.php/ijsp/article/view/46474
In this paper, we establish certain characterizations of theWeibull-X family of distributions proposed by Alzaatrehet al. (2013) as well as of the Burr XII Negative Binomial distribution, introduced by Ramos et al. (2015).These characterizations are based on two truncated moments, hazard rate function and conditional expectation offunctions of random variables.M. AhsanullahA. AlzaatrehI. GhoshG. G. Hamedani2015-04-222015-04-224Assessing Relative Importance Using RSP Scoring to Generate Variable Importance Factor (VIF)
http://ccsenet.org/journal/index.php/ijsp/article/view/46446
<p>Previous research has shown that the construction of VIF is challenging. Some researchers have sought to use orderly contribution of <em>R<sup>2</sup></em> (coefficient of determination) as measurement for relative importance of variable in a model, while others have sought the standardized parameter estimates <em>b</em> (beta) instead. These contributions have been proven to be very valuable to the literature. However, there is a lack of study in combining key properties of variable importance into one composite score. For example, an intuitive understanding of variable importance is by scoring reliability, significance and power (RSP) of it in the model. Thereafter the RSP scores can be aggregated together to form a composite score that reflects VIF. In this paper, the author seeks to prove the usefulness of the DS methodology. DS stands for Driver’s Score and is defined as the relative, practical importance of a variable based on RSP scoring. An industry data was used to generate DS for practical example in this paper. This DS is then translated into a 2x6 matrix where level of importance (L<em>x</em>I) is generated. The final outcome of this paper is to discuss the use of RSP scoring methodology, theoretical and practical use of DS and the possible future research that entails this paper. DS methodology is new to the existing literature.</p><p> </p>Daniel Koh2015-04-262015-04-264Best Predictive Generalized Linear Mixed Model with Predictive Lasso for High-Speed Network Data Analysis
http://ccsenet.org/journal/index.php/ijsp/article/view/48070
Optimizing network usage is important to maximize the network performance. When the network usage grows rapidly, it is important to build an accurate predictive model. We present a new predictive algorithm which can analyze the network performance in various network conditions and traffic patterns. Our approach is based on the best predictive generalized linear mixed model (GLMM). The parameters of the best predictive GLMM are estimated by minimizing the mean squared prediction error (MSPE). To expedite the parameter learning with the big data collected through the network, our algorithm introduced regularization, LASSO, and an innovative bootstrap. The merits of our new approach validated through data and simulation are that (1) the highest prediction accuracy even under a model misspecification; and (2) the least computation time compared to the Estimation-oriented GLMM with Lasso and Stepwise Selection GLMM. A major computational advantage of our method is that, unlike some of the current approaches, our method does not require the EM (Expectation-Maximization algorithm) procedure.Kejia HuJaesik ChoiAlex SimJiming Jiang2015-04-272015-04-274