http://www.ccsenet.org/journal/index.php/ijsp/issue/feedInternational Journal of Statistics and Probability2014-07-03T01:21:44-07:00Wendy Smithijsp@ccsenet.orgOpen Journal Systems<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and tacitly or explicitly by the responsible authorities where the work was carried out, and that, if accepted, will not be published elsewhere in the same form, in English or in any other language, without the written consent of the Publisher.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><em>International Journal of Statistics and Probability (IJSP) </em>is an open-access, international, double-blind peer-reviewed journal published by the <a href="/web/">Canadian Center of Science and Education</a>. <br /><br />This journal, published quarterly in both print and <a href="/journal/index.php/ijsp/issue/archive">online versions</a>, keeps readers up-to-date with the latest developments in all areas of statistics and probability.<br /><br />It is journal policy to publish work deemed by peer reviewers to be a coherent and sound addition to scientific knowledge and to put less emphasis on interest levels, provided that the research constitutes a useful contribution to the field.<br /><br />http://www.ccsenet.org/journal/index.php/ijsp/article/view/34438Asymptotic Efficiency of an Exponential Cure Model When Cure Information Is Partially Known2014-07-03T01:21:44-07:00Yu Wuhenry.wu@klserv.comYong Linlinyo@rutgers.eduChin-Shang Licssli@ucdavis.eduShou-En Lusl1020@sph.rutgers.eduWeichung Joe Shihshihwj@rutgers.eduCure models are popularly used to analyze failure time data where some individuals could eventually experience and others might never experience an event of interest. However in many studies, there are diagnostic procedures available to provide further information about whether a subject is cured. Wu et al. (2014) proposed a method, called the {\it extended} cure model, that incorporated such additional diagnostic cured status information into the classical cure model analysis. Through extensive simulations, they demonstrated that the extended cure models provide more efficient and less biased estimations, and higher efficiency and smaller bias are associated with higher sensitivity and specificity of the diagnostic procedure used. In this paper, we provide theoretical justifications of this positive association for some special cases. More specifically we shows that the maximum likelihood estimators (MLEs) of the parameters for an extended exponential cure model are asymptotically more efficient than the MLEs for the corresponding classical exponential cure model.2014-06-11T00:04:06-07:00http://www.ccsenet.org/journal/index.php/ijsp/article/view/35902Bayesian Approach Using Latent Variable for Zero Truncated Poisson Distribution: Application for Species-Area Relationship2014-07-03T01:21:44-07:00Claude Thiago Arrabalkarinapss@gmail.comMarinho Gomes de Andrade Filhokarinapss@gmail.comKarina Paula dos Santos Silvakarinapss@gmail.comIn ecology, understanding the species-area relationship (SARs) is extremely important to determine species diversity. SARs are fundamental to evaluate the impact in this diversity due to destruction of natural habitats, to create biodiversity maps and to determine the minimum area to preserve. In this study, the number of species is observed in different area sizes. These studies are referred in the literature through nonlinear models without assuming any distribution of the data. In this situation, it only makes sense to consider areas in which the number of species is greater than zero. As the dependent variable is a count data, we assume that this variable comes from a known distribution for discrete positive data. In this paper, we used the zero truncated poisson distribution (ZTP) to represent the probability distribution of the random variable ``species diversity" and we considered some nonlinear models to describe the relationship between species diversity and habitat area. Among the proposed models in literature, we considered the Arrhenius power function, Persistence function (P1 e P2), Negative Exponential and Chapman-Richards to describe the abundance of species. In this paper, we take a Bayesian approach to fit models. With the purpose of obtaining conditional distributions, we propose the use of latent variables to implement the Gibbs Sampler. In order to progress using the best possible models for data, a comparison of performance between models referred in this paper will be verified through the criteria Extended Akaike Information Criterion (EAIC), Extended Bayesian Information Criterion (EBIC), Deviance Information Criterion (DIC) and Conditional Predictive Ordinate Criterion (CPO). In addition to selecting the best model, it will also assist to define the best selection criterion.2014-06-11T00:07:15-07:00http://www.ccsenet.org/journal/index.php/ijsp/article/view/37770The Parameters Optimization of Filtered Derivative for Change Points Analysis2014-07-03T01:21:44-07:00Mohamed Elmimahamed_elmi_abdillahi@univ.edu.djLet $\mathbf{X} = ( X_1,X_2,\ldots,X_N )$ be a time series. That is a sequence random variable indexed by the time $t=(1,2,\ldots,N)$, we suppose that the parameters of $\mathbf{X}$ are piecewise constant. In other words, it exists a subdivision $\tau=(\tau_1< \tau_2<\ldots < \tau_K )$ such that $ X_i$ is a family of independent and identically distributed (i.i.d) random variables for $i \in (\tau_k,\tau_{k+1}] $, and $k = 0,1,\ldots,K$ where by convention $\tau_o=0$ and $\tau_{K+1}=N $. The preceding works such that (Bertrand, 2000) control the probability of false alarms for minimizing the probability of type I error of change point analysis. The novelty in this work is to control the number of false alarms. We give an bound of number of false alarms and the necessary condition for number of no detection. In other hand, we know the filtered derivative (Basseville \& Nikirov, 1993) depends the parameters such that the threshold and the window, we give in order to choose the optimal parameters. We compare the results of Filtered Derivative optimized parameters and the Penalized Square Error methods in particulary the adaptive method of (Lavielle \& Teyssi\`ere, 2006).2014-06-11T00:00:00-07:00http://www.ccsenet.org/journal/index.php/ijsp/article/view/36130Approximate Nonparametric Maximum Likelihood Estimation for Interval Censoring Model Case II (Running Head: NPMLE for Interval Censoring Case II)2014-07-03T01:21:44-07:00Ao Yuanyuanao@hotmail.comYizheng Weiyuanao@hotmail.comKepher Makambiyuanao@hotmail.comHongkun Wangyuanao@hotmail.comWe study the nonparametric maximum likelihood estimate of the distribution function in a type II interval censoring model. We propose an approximate solution of the problem under a technical assumption. Some basic asymptotic properties of the estimator are investigated.<br />2014-06-11T00:14:34-07:00http://www.ccsenet.org/journal/index.php/ijsp/article/view/38179A Pathwise Fractional One Compartment Intra-Veinous Bolus Model2014-07-03T01:21:44-07:00Nicolas Marienmarie@u-paris10.frTo extend the deterministic compartments pharmacokinetics models as diffusions seems not realistic on the biological side because the paths of these stochastic processes are not smooth enough. In order to extend the one compartment intra-veinous bolus models, this paper suggests to model the concentration process $C$ by a class of stochastic differential equations driven by a fractional Brownian motion of Hurst parameter belonging to $]1/2,1[$.<br /><br />The first part of the paper provides probabilistic and statistical results on the concentration process $C$: the distribution of $C$, a control of the uniform distance between $C$ and the solution of the associated ordinary differential equation, and consistent estimators of the elimination constant, of the Hurst parameter of the driving signal, and of the volatility constant.<br /><br />The second part of the paper provides applications of these theoretical results on simulated concentrations: a method to choose the parameters on small sets of observations, and simulations of the estimators of the elimination constant and of the Hurst parameter of the driving signal. The relationship between the quality of the estimations and the size/length of the sample is discussed.2014-06-26T00:00:00-07:00http://www.ccsenet.org/journal/index.php/ijsp/article/view/38180Statistical Inference for a Simple Constant Stress Model Based on Censored Sampling Data From the Kumaraswamy Weibull Distribution2014-07-03T01:21:44-07:00G. R. AL-Dayianaah_elhelbawy@hotmail.comA. A. EL-Helbawyaah_elhelbawy@hotmail.comH. R. Rezkaah_elhelbawy@hotmail.comIn this paper, constant stress accelerated life tests are discussed based on Type I and Type II censored sampling data from Kumaraswmay Weibull distribution. The maximum likelihood estimators are derived for the unknown parameters. The log linear model is assumed as an accelerated model. In addition, confidence intervals for the model parameters are constructed. Optimum test plans, are developed to minimize the generalized asymptotic variance of the maximum likelihood estimators of the model parameters. Monte Carlo simulation is carried out to illustrate the theoretical results of the maximum likelihood estimates, confidence intervals and optimum test plans.2014-06-26T00:00:00-07:00http://www.ccsenet.org/journal/index.php/ijsp/article/view/36992A Simulation Study Comparing Knot Selection Methods With Equally Spaced Knots in a Penalized Regression Spline2014-07-03T01:21:44-07:00Eduardo L. Montoyaemontoya2@csub.eduNehemias Ulloanehe_maya@yahoo.comVictoria Millertori_miller@rocketmail.com<span style="color: #000000;"></span>Penalized regression splines are a commonly used method to estimate complex non-linear relationships between two variables. The fit of a penalized regression spline to the data depends on the number of knots, knot placement, and the value of the smoothing parameter. In this paper, we use a simulation study to compare knot selection methods with equidistant knots in a penalized regression spline model. We found that one method generally performed better than others. The results provide guidance in selecting the number of equidistant knots in a penalized regression spline model.2014-06-26T01:14:54-07:00http://www.ccsenet.org/journal/index.php/ijsp/article/view/37529Marginal Methods for Multivariate Failure Times Under Event-Dependent Censoring2014-07-03T01:21:44-07:00Longyang Wurjcook@uwaterloo.caRichard J. Cookrjcook@uwaterloo.caMany chronic diseases put individuals at increased risk of several different types of adverse clinical events. Typically these events are combined to define composite events which are then used as the basis of treatment evaluation. A potentially more efficient approach is to conduct separate marginal assessments of the effect of treatment on each component and then to synthesize this information across each type of event. While there is considerable potential for more powerful tests of treatment effect in this setting, it is possible that dependent censoring can cause problems. This happens when the occurrence of one type of event increases the risk of withdrawal from a study and hence alters the probability of observing events of other types. The purpose of this article is to formulate a model which reflects this type of mechanism, to evaluate the effect on the asymptotic and finite sample properties of marginal estimates, and to examine the performance of estimators obtained using flexible inverse probability weighted marginal estimating equations. Data from a motivating study are used for illustration.2014-07-03T01:20:33-07:00