International Journal of Statistics and Probability
http://www.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><li><strong>Ulrich's</strong></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and tacitly or explicitly by the responsible authorities where the work was carried out, and that, if accepted, will not be published elsewhere in the same form, in English or in any other language, without the written consent of the Publisher.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>Modeling a Mixture of Linear and Changepoint Trajectories for Longitudinal Time-Series Data
http://www.ccsenet.org/journal/index.php/ijsp/article/view/46121
Longitudinal changepoint data naturally arise in many applications. Examples include transition of core body temperature following the hypothermia therapy and prostate-specific antigen levels following treatment. Note that the trend change occurs due to a shock (e.g., treatment) to the system. Thus, an individual exhibiting a linear trend could be an indication of insignificant effects of the shock. One of the goals of this type of study is to investigate whether the shock is significantly associated in changing the trend of a trajectory. The bent-cable model characterizes the shock-through data using three phases: (a) an incoming phase characterizing the trend before the shock comes into effect, (b) a transition due to the shock, and (c) an outgoing phase due to the after-shock effects. In this article, we develop bent-cable methodology accounting for trajectories exhibiting either a linear trend or a trend change characterized by gradual or abrupt transition.Shahedul Khan2015-07-012015-07-014Some Generalized Families of Weibull Distribution: Properties and Applications
http://www.ccsenet.org/journal/index.php/ijsp/article/view/47078
<p>The Weibull distribution has been applied in various fields, especially to fit life time data. Some of these applications are limited partly due to the fact that the distribution has monotonically increasing, monotonically decreasing or constant hazard rate. This limitation undoubtedly inspired researchers to develop generalized Weibull distribution that can exhibit unimodal or bathtub hazard rate. In this article, we introduce six new families of <em>T</em>-Weibull{<em>Y</em>} distributions arising from the quantile function of a random variable <em>Y</em>. These six families are: The <em>T</em>-Weibull{uniform}, <em>T</em>-Weibull{exponential}, <em>T</em>-Weibull{log-logistic}, <em>T</em>-Weibull{Fréchet}, <em>T</em>-Weibull{logistic} and <em>T</em>-Weibull{extreme value}. Some properties of these families are discussed and general expressions for the quantile function, the Shannon’s entropy, the non-central moments and the mean deviations are provided. Different new members of the <em>T</em>-Weibull{<em>Y</em>} families are derived and some of their properties are discussed. Two real data sets are used to illustrate the potential usefulness of the <em>T</em>-Weibull{<em>Y</em>} distributions and the results are compared with the results from some existing distributions.</p>Maalee AlmheidatFelix FamoyeCarl Lee2015-07-012015-07-014Generalized Likelihood Ratio Tests Based on The Asymptotic Variant of The Minimax Approach
http://www.ccsenet.org/journal/index.php/ijsp/article/view/47092
Maximum likelihood ratio test statistics may not exist in general in nonparametric function estimation setting. In this paper a new class of generalized likelihood ratio (GLR) tests is proposed for nonparametric goodness-of-fit testing via the asymptotic variant of the minimax approach. The proposed nonparametric tests are developed to be asymptotically distribution-free based on latent variable representations. The nonparametric tests are ameliorated to be appropriately complex so that they are analytically tractable and numerically feasible. They are well applicable for the ``adaptive" study of hypothesis testing problems of growing dimensions. To assess the proposed GLR tests, the asymptotic properties are derived. The procedure can be viewed as a novel nonparametric extension of the classical parametric likelihood ratio test as a guard against possible gross misspecification of the data-generating mechanism. Simulations of the proposed minimax-type GLR tests are investigated for the small sample size performance and show that the GLR tests have appealing small sample size properties.Han Yu2015-07-012015-07-014Characterizations of Probability Distributions with Completely Monotone Hazard Functions
http://www.ccsenet.org/journal/index.php/ijsp/article/view/47364
<p>In this article, we characterize the classes of absolutelycontinuous distributions concentrated on $(0, \infty)$ anddiscrete distributions concentrated on $\{0,1,2, ...\}$, with(non-vanishing survivor functions having) completely monotonehazard functions; in the latter case, we refer to the hazardfunctions also as the hazard sequences. These provide us withcharacterizations of the certain specialized versions of mixturesof exponential and geometric distributions with mixingdistributions, satisfying some further criteria, which by theGoldie-Steutel theorem and a result of Kaluza are seen to bespecialized versions of infinitely divisible distributions. Weshed light on the implications of our findings, giving somepertinent examples and remarks.</p>Mohammed Albassam2015-07-012015-07-014Unbiased Estimation for Linear Regression When n < v
http://www.ccsenet.org/journal/index.php/ijsp/article/view/47855
In this paper a new method is proposed for solving <p style="text-indent: 0px; margin: 0px;">the linear regression problem when the number of observations $n$</p> <p style="text-indent: 0px; margin: 0px;">is smaller than the number of predictors v. This method uses the</p> <p style="text-indent: 0px; margin: 0px;">idea of graphical models and provides unbiased parameter estimates</p> <p style="text-indent: 0px; margin: 0px;">under certain conditions, while existing methods such as ridge</p> <p style="text-indent: 0px; margin: 0px;">regression, LASSO and least angle regression (LARS) give biased</p> <p style="text-indent: 0px; margin: 0px;">estimates. Also the new method can provide a detailed graphical</p> <p style="text-indent: 0px; margin: 0px;">correlation structure for the predictors, therefore the real</p> <p style="text-indent: 0px; margin: 0px;">causal relationship between predictors and response could be</p> <p style="text-indent: 0px; margin: 0px;">identified. In contrast, existing methods often cannot identify</p> <p style="text-indent: 0px; margin: 0px;">the real important predictors which have possible causal effects</p> <p style="text-indent: 0px; margin: 0px;">on the response variable. Unlike the existing methods based on graphical models, the proposed method can identify the potential networks while doing regression even if the data do not follow a multivariate distribution. The new method is compared with some existing methods such as ridge regression, LASSO and LARS by using simulated and real data sets. Our experiments reveal that the new method outperforms all the other methods when n<v.</p>Saeed AldahmaniHongsheng Dai2015-07-012015-07-014Regularized Single Index Quantile Regression Model
http://www.ccsenet.org/journal/index.php/ijsp/article/view/48894
<pre><!--StartFragment-->This article proposes a new approach for variable selection in the single index <span>quantile</span> regression model. Compared to existing methods, the new approach produce sparse solutions for the index vector. Performance of the new method is enhanced by a fully adaptive penalty function. Finite sample performance is studied through a simulation study that compares the proposed method with existing work under several criteria. A data analysis is given which highlights the usefulness of the proposed methodology.<!--EndFragment--></pre>Chinthaka Kuruwita2015-07-012015-07-014On the Detection of Heteroscedasticity by Using CUSUM Range Distribution
http://www.ccsenet.org/journal/index.php/ijsp/article/view/50691
In this paper, we present a new method for checking the heteroscedasticity among the error terms. The method is based on the CUSUM Range distribution. We derive the CUSUM Range distribution (under the assumption of homogeneity) and use it to test for heteroscedasticity. The method seems to detect heteroscedasticity when it is present among the error terms.A. NanthakumarS. KanburE. Wilson2015-07-012015-07-014Kumaraswamy-Half-Cauchy Distribution: Characterizations and Related Results
http://www.ccsenet.org/journal/index.php/ijsp/article/view/50692
We present various characterizations of a recently introduced distribution (Ghosh2014), called Kumaraswamy-Half- Cauchy distribution based on: $\left(i\right) $ a simple relation between two truncated moments; $\left(ii\right) $ truncated moment of certain function of the $1^{st}$ \ orderstatistic; $\left( iii\right) $ truncated moment of certain function of therandom variable; $\left( iv\right) $ hazard function; $\left( v\right) $distribution of the $1^{st}$ \ order statistic; $\left( vi\right) $\ viarecord values. \ We also provide some remarks on bivariate Gumbel copuladistribution whose marginal distributions are Kumaraswamy- Half-Cauchy distributions.G.G. HamedaniI. Ghosh2015-07-012015-07-014Tournament Seeding Efficiency and Home Court Advantage: College Basketball’s National Invitation Tournament
http://www.ccsenet.org/journal/index.php/ijsp/article/view/47409
<p>The relationship between seeding and outcomes in the Men’s NCAA Basketball Tournament has been explored by a number of relatively recent studies. However, there has been very little published research on the Men’s Postseason National Invitation Tournament, which, unlike contests in the former tournament, are typically played on a home court basis. As such, the relationship between seeding and expected outcomes may differ between the two events. Results from linear probability and probit models presented here indicate that, although the intercept is higher as expected, the marginal effect of a 1-unit seeding differential in an NCAA Tournament contest is only about 60-75 percent of its NIT contest counterpart.</p>Jeremy PhillipsSteven B. CaudillFranklin G. Mixon2015-07-092015-07-094Semiparametric Marginal Models for Binary Longitudinal Data
http://www.ccsenet.org/journal/index.php/ijsp/article/view/48546
In this paper, we propose and explore a semiparametric approach to analyzing longitudinal binary data often observed in clinical studies. We applied second-order GEE approach to analyze longitudinal binary responses based on a partially linear single-index model. We use a local polynomial smoothing technique to estimate the single-index. We study the empirical properties of the proposed estimators using simulations. The empirical results demonstrate that if the true underlying model is partially linear, then our proposed method generally provides unbiased and efficient estimators. The proposed method is also applied to some real data sets obtained from longitudinal studies.Salehin K. ChowdhurySanjoy K. Sinha2015-07-092015-07-094Characterizations of Distributions via Conditional Expectation of Generalized Order Statistics
http://www.ccsenet.org/journal/index.php/ijsp/article/view/49073
Characterizations of probability distributions by different regression conditions on generalized order statistics has attracted the attention of many researchers. We present here, characterizations of certain continuous distributions based on the conditional expectation of generalized order statistics.M. AhsanullahG. G. HamedaniM. Maadooliat2015-07-092015-07-094Comparison of Means of Two Log-Normal Distributions when Data is Multiply Censored
http://www.ccsenet.org/journal/index.php/ijsp/article/view/50977
When measuring concentration of chemical compounds, we often haveto deal with a situation when the resulting values are found belowthe detection limit of the determination method. In order tostatistically evaluate such data, the newly developed method ofmaximum likelihood considering multiply left-censored samples isapplied. This paper is motivated by the need to have validinference concerning the equality of the means of two log-normaldistributions that are frequently encountered in environmental andexposure data analysis. As a model distribution of measuredenvironmental and/or biomedical data, log-normal distribution isconsidered. Moreover, using the asymptotic properties of maximumlikelihood estimates, concentrations of chemicals can be compared.A test procedure for comparing the means of two independentlog-normal populations in the presence of multiply censored datais also introduced and evaluated. Asymptotic chi-square test isused in the proposed test procedure. Worked example is given illustrating the use of the methodsprovided utilizing a computer program written in the R language. Asimulation study was performed to examine the power and the sizeof the proposed test procedure introduced in this article.Abou El-Makarim A. Aboueissa2015-07-102015-07-104On Periodic Maintenance of a Coherent System
http://www.ccsenet.org/journal/index.php/ijsp/article/view/51057
In this paper, we study a coherent system that has periodic maintenance performed at regular intervals. The exact analytical expressions are obtained for some important maintenance performance measures such as mean time between failures, average availability and mean fractional dead time. The CHA algorithm is used to do the relevant calculations. Some s-coherent structures viz., series, parallel, 2-out-of-3:G and a fire-detector system are considered to illustrate the method.G Chaudhuri2015-07-142015-07-144A Note on $\mathbb{L}_{2}$-structure of Continuous-time Bilinear Processes with Time-varying Coefficients
http://www.ccsenet.org/journal/index.php/ijsp/article/view/51242
This paper is concerned with the investigation of $\mathbb{L}_{2}$-structureissue of time-varying coefficients continuous-time bilinear processes ($COBL$)driven by a Brownian motion $\left(BM\right)$. Such processes are veryuseful for modeling irregular spacing non linear and non Gaussian datasets andmay be proposed to model for instance some financial returns representing highamplitude oscillations and thus make it a serious candidate for describeprocesses with time-varying degree of persistence and other complex systems.Our attention is focused however on the probabilistic structure of $COBL$processes, so, we establish necessary and sufficient conditions for theexistence of regular solutions in term of their transfer function. Expliciteformulas for the mean and covariance functions are given. As a consequence, weobserve that the second order structure is similar to a $CARMA$ processes withsome uncorrelated noise. Therefore, it is necessary to look intohigher-order cumulant in order to distinguish between $COBL$ and $CARMA$ processes.Abdelouahab BibiFateh Merahi2015-07-202015-07-204Novel Scale Development for Fear of Falling and Falls: Analysed Using a Semiparametric Ratio Estimator (SPRE)
http://www.ccsenet.org/journal/index.php/ijsp/article/view/50127
<p>Fear of falling (fof) and falls are increasingly severe worldwide public health problems. The Falls Weight Function (FWF) uses a new scale to incorporate fear of falling (fof) into analyses with participants who have already experienced a fall. FWF is a weight function in the semiparametric ratio estimator (SPRE) to predict a change point and point estimations. FWF data is a discrete set of numbers that is finite or countable. In a study using Stepping On® fall prevention program, initial data from fof responses were counted, summed as increments of .10 values (ranging from .1 to 1.0), and then multiplied by 1fall. The un-weighted value of 1 fall was multiplied by the weight function for fof. Then, the scale of falls and fof is the same, and represented on a continuum from fear of falling to having a fall, so that all participants can be treated and analyzed together.</p>Deborah Weissman-MillerKay C. Graham2015-07-212015-07-214A Multi-stages Decision Approach for Managerial Flexibility of Energy R&D Project under Fuzzy Environment
http://www.ccsenet.org/journal/index.php/ijsp/article/view/51350
In recent years, many countries and firms seek the new and renewable energy to cope with the impending global environmental crisis, such as depletion of fossil-based energy, climate change to control emissions of greenhouse gases. This paper aims to take the perspective of the firm, which undertakes the energy R\&D project to maximize profits implying minimization of total cost as well. Incorporating technical and market risks into energy R\&D project is crucial, in that the managers often face the rapidly changing environment full of uncertainties. The firms should incorporate managerial flexibility into energy R\&D project decision not only reducing uncertain risks, but also increasing potential market payoff. This research considers a multi-stages decision model in which real-option-based analysis is applied for energy R\&D project under fuzzy environment. Specifically, the market payoff is obtained when the new and renewable energy product is commercialized to market, while energy R\&D investment costs are exhausted gradually. Furthermore, the uncertain development performance and market information are described as fuzzy variables by credibility theory. Instead of the traditional real option pricing methods, the dynamic programming methodology that captures the uncertain product development performance and final market return is developed to more effectively characterize the managerial flexibility. This method can reflect the multi-stages nature of R\&D programme, while helping decision-makers take the optimal investment decision and capture future market opportunities of energy products.Changsheng YiQiumei Jin2015-07-242015-07-244Students’ Emerging Reasoning about Data Tables of Large-Scale Data
http://www.ccsenet.org/journal/index.php/ijsp/article/view/50246
This study investigated thirty-two Year 9 secondary school students’ (15 year olds) reasoning about data tables of large-scale data. Eight groups of four students, drawn from six classes, participated in a workshop that examined the components of population change for EU and candidate countries, namely natural increase of population, net overseas migration for Europe and their country, and total population growth. Students investigated trends in real data displayed in tables, and responded to a set of reflective questions. Analysis of the reasoning used by the students revealed four levels of data-table comprehension—reading the data, reading within the data, reading beyond the data, and reading behind the data—similar to the levels described for students working with smaller data sets.Theodosia Prodromou2015-07-232015-07-234