International Journal of Statistics and Probability, Issue: Vol.8, No.2IJSPFri, 19 Apr 2019 08:16:57 +0000Zend_Feed_Writer 2 (http://framework.zend.com)
http://www.ccsenet.org/journal/index.php/ijsp
ijsp@ccsenet.org (International Journal of Statistics and Probability)International Journal of Statistics and ProbabilityM/M/1 Model With Unreliable Service and a Working VacationWe derive an explicit closed form of the stationary distribution of an M/M/1 queue with unreliable service and a working vacation. We also show that the work in (Patterson & Korzeniowski, 2018) can be obtained as a special case of this model. Future work remains to be done; specifically, it may be possible to use the explicit stationary distribution given here to decompose the queue length into the sum of independent random variables. Consequently, it may then be possible to utilize Little’s Law (Little, 1961) to decompose the customer waiting time as well.]]>Mon, 11 Mar 2019 01:59:43 +0000
http://www.ccsenet.org/journal/index.php/ijsp/article/view/0/38162
http://www.ccsenet.org/journal/index.php/ijsp/article/view/0/381620Boosted Convolutional Decision Trees for Translationally Invariant Pattern Recognition and Transfer LearningDecision Tree (DT) models provide a well-known class of interpretable machine learning tools for diverse pattern recognition problems. However, applying DTs to learn floating features in images and categorical data based on their raw representation has been challenging. Convolutional Neural Networks (CNNs) are the current state-of-the-art method for classifying raw images, but have their own disadvantages, including that they are often difficult to interpret, have a large number of parameters and hyperparameters, require a fixed image size, and have only partial translational invariance directly built into its architecture. We propose a novel application of Convolutional Decision Trees (CDTs) and show that our approach is more interpretable and can learn higher quality convolutional filters compared to CNNs. CDTs have full translational invariance built into the architecture and can be trained and make predictions on variable-sized images. Using two independent test cases—protein-DNA binding prediction, and hand-written digit classification—we demonstrate that our GPU-enabled implementation of the Cross Entropy (CE) optimization method for training CDTs learns informative convolutional filters that can both facilitate accurate data classifications in a tree-like pattern and be used for transfer learning to improve CNNs themselves. These results motivate further studies on developing accurate and efficient tree-based models for pattern recognition and computer vision.]]>Mon, 14 Jan 2019 09:27:44 +0000
http://www.ccsenet.org/journal/index.php/ijsp/article/view/0/38163
http://www.ccsenet.org/journal/index.php/ijsp/article/view/0/381630A Composite Likelihood Method for the Analysis of Multivariate Survival Data: An Application to a PBDE StudyWhen dealing with multivariate survival data, featuring the association structure is a key difference from the univariate survival analysis. In this paper, we explore to use the composite likelihood framework to handle multivariate survival data, where only the lower dimensional survival distributions need to be specified. The development allows us to use available modeling schemes for bivariate survival data to characterize association structures of correlated survival times. The inference procedure is based on the pseudolikelihood which is the product of the lower dimensional bivariate distributions. The proposed estimation procedure is assessed through simulation studies. As a genuine application, we apply the composite likelihood inference procedure to analyze the data from the polybrominated diphenyl ethers (PBDEs) study, where four types of PBDE congeners are available. The associations among the four PBDE congeners, and the relationships between the covariates and the PBDE congeners are of interest. The result shows that there is strong association among the concentrations of the four PBDE congeners, and statistically significant predictors on the concentrations of the four PBDE congeners are identified.]]>Mon, 14 Jan 2019 10:17:36 +0000
http://www.ccsenet.org/journal/index.php/ijsp/article/view/0/38164
http://www.ccsenet.org/journal/index.php/ijsp/article/view/0/381640Bayesian Joint Models for Longitudinal and Multi-state Survival DataThu, 17 Jan 2019 03:00:39 +0000
http://www.ccsenet.org/journal/index.php/ijsp/article/view/0/38165
http://www.ccsenet.org/journal/index.php/ijsp/article/view/0/381650Extended Poisson-Log-Logistic DistributionIn this work, we introduce a new Poisson-log-logistic distribution with a physical interpretation and some applications. Some essential properties are derived. Modeling of four real data sets are provided to illustrate the wide applicability of the new model in differnt fields like finance, reliability, economy and medicine. The new compound model is better than other well-known competitive models which have at least the same number of parameters.]]>Wed, 16 Jan 2019 03:12:29 +0000
http://www.ccsenet.org/journal/index.php/ijsp/article/view/0/38166
http://www.ccsenet.org/journal/index.php/ijsp/article/view/0/381660The Odd Power Lindley Generator of Probability Distributions: Properties, Characterizations and Regression ModelingIn this study, a new flexible family of distributions is proposed with its statistical properties as well as some useful characterizations. The maximum likelihood method is used to estimate the unknown model parameters by means of two simulation studies. A new regression model is proposed based on a special member of the proposed family called, the log odd power Lindley Weibull distribution. Residual analysis is conducted to evaluate the model assumptions. Four applications to real data sets are given to demonstrate the usefulness of the proposed model.]]>Fri, 25 Jan 2019 09:29:36 +0000
http://www.ccsenet.org/journal/index.php/ijsp/article/view/0/38322
http://www.ccsenet.org/journal/index.php/ijsp/article/view/0/383220Mechanical Proof of the Maxwell Speed DistributionWed, 30 Jan 2019 07:47:11 +0000
http://www.ccsenet.org/journal/index.php/ijsp/article/view/0/38323
http://www.ccsenet.org/journal/index.php/ijsp/article/view/0/383230A Review of the Methodologies Used in the Derivation of Formulas for Parametric Survival Functions with Illustrative Numerical ExamplesIn this review paper formulas for survival functions are derived that take into account risks of deaths in early life including infancy, mid life, a random component of deaths due to accidents and deaths in older ages. The basic ideas used in the derivation of survival function for each of the components just mentioned are risk functions. Given a formula for a risk function, it is possible to derive a formula for the corresponding survival function. By using the theory of competing risks, a formula for survival function that takes into account the risks of deaths in various stages of life expressed as a product of survival functions for the risks of deaths under consideration. For many applications information on the numerical values of parameters in survival functions is not available. Consequently, rationales are developed for assigning plausible values to parameters that take into account personal ideas of an investigator may have for each stage of life. For every assignment of parameter values in the paper, a numerical version of survival functions are plotted in graphs so that an assessment of the plausibility of the chosen parameter values may be made. Also included in the paper is an application of survival functions in an experiment to make an assessment as to whether a small population of chimpanzees, or some other endangered species of animals, will have descendants that make up a surviving population 200 years into the future.]]>Thu, 28 Feb 2019 03:39:22 +0000
http://www.ccsenet.org/journal/index.php/ijsp/article/view/0/38353
http://www.ccsenet.org/journal/index.php/ijsp/article/view/0/383530Estimation of the Parameters and Expected Test Time of Exponentiated Weibull Lifetimes Under Type II Progressive Censoring Scheme With Random RemovalsBased on progressive type-II censored sample with random removals, point and interval estimations for the shape parameters of the exponentiated Weibull distribution are discussed. Computational formula for the expected total test time are derived for different situations of sampling plans. This is useful in planning a life test experiment. The efficiency of the estimators are compared in terms of the root mean square error, the variance and the coverage probability of the corresponding confidence intervals. A simulation study is presented for several values of removal probability and different values of failure percentage. Also, numerical applications are conducted to illustrate and compare the usefulness of the different sampling plans in terms of expected test times for different patterns of failure rates.]]>Thu, 28 Feb 2019 03:42:59 +0000
http://www.ccsenet.org/journal/index.php/ijsp/article/view/0/38481
http://www.ccsenet.org/journal/index.php/ijsp/article/view/0/384810Measure of Departure From Local Symmetry for Square Contingency TablesFor square contingency tables, this paper considers the local symmetry model which indicates that there is a symmetric structure of probabilities for only one of pairs of symmetric cells. Also it proposes the measure to express the degree of departure from the local symmetry model. The measure is expressed as the weighted harmonic mean of the diversity index including the Shannon entropy. Examples are given.]]>Tue, 12 Feb 2019 08:08:08 +0000
http://www.ccsenet.org/journal/index.php/ijsp/article/view/0/38482
http://www.ccsenet.org/journal/index.php/ijsp/article/view/0/384820Extended Poisson Inverse Weibull Distribution: Theoretical and Computational AspectsA new extension of the Poisson Inverse Weibull distribution is derived and studied in details. Number of structural mathematical properties are derived. We used the well-known maximum likelihood method for estimating the model parameters. The new model is applied for modeling some real data sets to prove its importance and flexibility empirically.]]>Thu, 28 Feb 2019 03:46:54 +0000
http://www.ccsenet.org/journal/index.php/ijsp/article/view/0/38507
http://www.ccsenet.org/journal/index.php/ijsp/article/view/0/385070Iterative Approaches to Handling Heteroscedasticity With Partially Known Error VariancesHeteroscedasticity plays an important role in data analysis. In this article, this issue along with a few different approaches for handling heteroscedasticity are presented. First, an iterative weighted least square (IRLS) and an iterative feasible generalized least square (IFGLS) are deployed and proper weights for reducing heteroscedasticity are determined. Next, a new approach for handling heteroscedasticity is introduced. In this approach, through fitting a multiple linear regression (MLR) model or a general linear model (GLM) to a sufficiently large data set, the data is divided into two parts through the inspection of the residuals based on the results of testing for heteroscedasticity, or via simulations. The first part contains the records where the absolute values of the residuals could be assumed small enough to the point that heteroscedasticity would be ignorable. Under this assumption, the error variances are small and close to their neighboring points. Such error variances could be assumed known (but, not necessarily equal).The second or the remaining portion of the said data is categorized as heteroscedastic. Through real data sets, it is concluded that this approach reduces the number of unusual (such as influential) data points suggested for further inspection and more importantly, it will lowers the root MSE (RMSE) resulting in a more robust set of parameter estimates.]]>Mon, 04 Mar 2019 02:14:10 +0000
http://www.ccsenet.org/journal/index.php/ijsp/article/view/0/38531
http://www.ccsenet.org/journal/index.php/ijsp/article/view/0/385310Cavitation and Negative Pressure: A Flexible Water Model Molecular Dynamics SimulationThe critical negative pressure for cavitation in water has been theoretically predicted to be in the range of -100 to -200 MPa at room temperature, whereas values around -30 MPa have been obtained by many experiments. The discrepancy has yet to be resolved. Molecular dynamics (MD) is an effective method of observing bubble nucleation, however, most MD simulations use a rigid water model and do not take the effects of intermolecular vibrations into account. In this manuscript we perform MD simulations to study cavitation in water by using a TIP4P/2005f model under volumecontrolled stretching. It is found that the critical negative pressure of water was -168 MPa in the simulation and the critical negative pressure of water containing 50 oxygen molecules was -150 MPa. Hydrogen bonds played a major role in the cavitation process: the breaking of hydrogen bonds promoted bubble generation and growth. The O-H bond could release energy to increase the amount of potential energy in the system, so that cavitation was more likely to occur. When cavitation occurred, the O-H bond could absorb energy to reduce the amount of potential energy in the system, which will promote the growth of bubbles, and stabilise the cavitation bubbles.]]>Fri, 22 Feb 2019 00:42:09 +0000
http://www.ccsenet.org/journal/index.php/ijsp/article/view/0/38532
http://www.ccsenet.org/journal/index.php/ijsp/article/view/0/385320Principal Component Analysis and Its Derivation From Singular Value DecompositionGenerally, today data analysts and researchers are often faced with a daunting task of reducing high dimensional datasets as large volume of data can be easily generated given the explosive activities of the internet. The most widely used tools for data reduction is the principal component analysis. Merely in some cases, the singular value decomposition method is applied. The study examined the application and theoretical framework of these methods in terms of its linear algebra foundation. The study discovered that the SVD method is a more robust and general method for a change of basis and low rank approximations. But.in terms of application, the PCA method is easy to interpret as illustrated in the work.]]>Fri, 22 Feb 2019 00:49:52 +0000
http://www.ccsenet.org/journal/index.php/ijsp/article/view/0/38533
http://www.ccsenet.org/journal/index.php/ijsp/article/view/0/385330Reviewer Acknowledgements for International Journal of Statistics and Probability, Vol. 8, No. 2Thu, 28 Feb 2019 06:27:42 +0000
http://www.ccsenet.org/journal/index.php/ijsp/article/view/0/38637
http://www.ccsenet.org/journal/index.php/ijsp/article/view/0/386370