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Recent documents in DigitalCommons@WayneStateen-usFri, 19 Dec 2014 01:30:52 PST3600Classical and Motivic Adams-Novikov Charts
http://digitalcommons.wayne.edu/math_reports/95
http://digitalcommons.wayne.edu/math_reports/95Wed, 17 Dec 2014 06:01:35 PST
This document contains large-format Adams-Novikov charts that compute the classical 2-complete stable homotopy groups. The charts are essentially complete through the 59-stem. We believe that these are the most accurate and extensive charts of their kind. We also include a motivic Adams-Novikov E∞ chart.
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Daniel C. IsaksenClassical and Motivic Adams Charts
http://digitalcommons.wayne.edu/math_reports/94
http://digitalcommons.wayne.edu/math_reports/94Wed, 17 Dec 2014 06:01:34 PST
This document contains large-format Adams charts that compute 2-complete stable homotopy groups, both in the classical context and in the motivic context over C. The charts are essentially complete through the 59-stem and contain partial results to the 70-stem. In the classical context, we believe that these are the most accurate charts of their kind. We also include Adams charts for the motivic homotopy groups of the cofiber of τ.
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Daniel C. IsaksenVol. 13, No. 2 (Full Issue)
http://digitalcommons.wayne.edu/jmasm/vol13/iss2/33
http://digitalcommons.wayne.edu/jmasm/vol13/iss2/33Tue, 09 Dec 2014 13:29:15 PST
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JMASM EditorsEnd Matter
http://digitalcommons.wayne.edu/jmasm/vol13/iss2/32
http://digitalcommons.wayne.edu/jmasm/vol13/iss2/32Tue, 09 Dec 2014 13:29:14 PST
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JMASM EditorsFitting Stereotype Logistic Regression Models for Ordinal Response Variables in Educational Research (Stata)
http://digitalcommons.wayne.edu/jmasm/vol13/iss2/31
http://digitalcommons.wayne.edu/jmasm/vol13/iss2/31Tue, 09 Dec 2014 13:29:13 PST
The stereotype logistic (SL) model is an alternative to the proportional odds (PO) model for ordinal response variables when the proportional odds assumption is violated. This model seems to be underutilized. One major reason is the constraint of current statistical software packages. Statistical Package for the Social Sciences (SPSS) cannot perform the SL regression analysis, and SAS does not have the procedure developed to directly estimate the model. The purpose of this article was to illustrate the stereotype logistic (SL) regression model, and apply it to estimate mathematics proficiency level of high school students using Stata. In addition, it compared the results of fitting the PO model and the SL model. Data from the High School Longitudinal Study of 2009 (HSLS: 2009) (Ingels, et al., 2011) were used for the ordinal regression analyses.
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Xing LiuLocal Bandwidths for Improving Performance Statistics of Model-Robust Regression 2
http://digitalcommons.wayne.edu/jmasm/vol13/iss2/30
http://digitalcommons.wayne.edu/jmasm/vol13/iss2/30Tue, 09 Dec 2014 13:29:11 PST
Model-Robust Regression 2 (MRR2) method is a semi-parametric regression approach that combines parametric and nonparametric fits. The bandwidth controls the smoothness of the nonparametric portion. We present a methodology for deriving data-driven local bandwidth that enhances the performance of MRR2 method for fitting curves to data generated from designed experiments.
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Efosa N. Edionwe et al.Bayesian Inference for Volatility of Stock Prices
http://digitalcommons.wayne.edu/jmasm/vol13/iss2/29
http://digitalcommons.wayne.edu/jmasm/vol13/iss2/29Tue, 09 Dec 2014 13:29:10 PST
Lognormal distribution is widely used in the analysis of failure time data and stock prices. Maximum likelihood and Bayes estimator of the coefficient of variation of lognormal distribution along with confidence/credible intervals are developed. The utility of Bayes procedure is illustrated by analyzing prices of selected stocks.
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Juliet G. D'Cunha et al.Estimates and Forecasts of GARCH Model under Misspecified Probability Distributions: A Monte Carlo Simulation Approach
http://digitalcommons.wayne.edu/jmasm/vol13/iss2/28
http://digitalcommons.wayne.edu/jmasm/vol13/iss2/28Tue, 09 Dec 2014 13:29:08 PST
The effect of misspecification of correct sampling probability distribution of Generalized Autoregressive Conditionally Heteroscedastic (GARCH) processes is considered. The three assumed distributions are the normal, Student t, and generalized error distributions. The GARCH process is sampled using one of the distributions and the model is estimated based on the three distributions in each sample. Parameter estimates and forecast performance are used to judge the estimated model for performance. The AR-GARCH-GED performed better on the three assumed distributions; even, when Student t distribution is assumed, AR-GARCH-Student t does not perform as the best model.
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OlaOluwa S. Yaya et al.Missing Data and the Statistical Modeling of Adolescent Pregnancy
http://digitalcommons.wayne.edu/jmasm/vol13/iss2/27
http://digitalcommons.wayne.edu/jmasm/vol13/iss2/27Tue, 09 Dec 2014 13:29:07 PST
Missing data is a pervasive problem in social science research. Many techniques have been developed to handle the problem. Different ways of handling missing data were shown to lead to different results in statistical models. A demonstration was given based on statistical modeling of the likelihood of a woman reporting having had an adolescent pregnancy by handling missing data with several different approaches. Results indicate that many of the independent variables in the model vary in whether they are, or are not, statistically significant in predicting the log odds of a woman having a teen pregnancy, and in the ranking of the magnitude of their relative effects on the outcome.
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Dudley L. Poston Dr. et al.Optimal Location Design for Prediction of Spatial Correlated Environmental Functional Data
http://digitalcommons.wayne.edu/jmasm/vol13/iss2/26
http://digitalcommons.wayne.edu/jmasm/vol13/iss2/26Tue, 09 Dec 2014 13:29:05 PST
The optimal choice of sites to make spatial prediction is critical for a better understanding of really spatio-temporal data. It is important to obtain the essential spatio-temporal variability of the process in determining optimal design, because these data tend to exhibit both spatial and temporal variability. Two new methods of prediction for spatially correlated functional data are considered. The first method models spatial dependency by fitting variogram to empirical variogram, similar to ordinary kriging (univariate approach). The second method models spatial dependency by linear model co-regionalization (multivariate approach). The variance of prediction method was chosen as the optimization design criterion. An application to CO concentration forecasting was conducted to examine possible differences between the design and the optimal design without considering temporal structure.
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Mahdi Rasekhi et al.The Information Criterion
http://digitalcommons.wayne.edu/jmasm/vol13/iss2/25
http://digitalcommons.wayne.edu/jmasm/vol13/iss2/25Tue, 09 Dec 2014 13:29:04 PST
The Akaike information criterion, AIC, is widely used for model selection. Using the AIC as the estimator of asymptotic unbias for the second term Kullbake-Leibler risk considers the divergence between the true model and offered models. However, it is an inconsistent estimator. A proposed approach the problem is the use of A'IC, a consistently offered information criterion. Model selection of classic and linear models are considered by a Monte Carlo simulation.
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Masume GhahramaniEstimation of Gumbel Parameters under Ranked Set Sampling
http://digitalcommons.wayne.edu/jmasm/vol13/iss2/24
http://digitalcommons.wayne.edu/jmasm/vol13/iss2/24Tue, 09 Dec 2014 13:29:02 PST
Consider the MLEs (maximum likelihood estimators) of the parameters of the Gumbel distribution using SRS (simple random sample) and RSS (ranked set sample) and the MOMEs (method of moment estimators) and REGs (regression estimators) based on SRS. A comparison between these estimators using bias and MSE (mean square error) was performed using simulation. It appears that the MLE based on RSS can be a robust competitor to the MLE based on SRS.
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Omar M. Yousef et al.Contrast of Bayesian and Classical Sample Size Determination
http://digitalcommons.wayne.edu/jmasm/vol13/iss2/23
http://digitalcommons.wayne.edu/jmasm/vol13/iss2/23Tue, 09 Dec 2014 13:29:01 PST
Sample size determination is a prerequisite for statistical surveys. A comprehensive overview of the Bayesian approach for computation of the sample size, and a comparison with classical approaches, is presented. Two surveys are taken as example to illustrate the accuracy and efficiency of each approach, and to make recommendations about which method is preferred. The Bayesian approach of sample size determination may require fewer subjects if proper prior information is available.
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Farhana Sadia et al.Double Bootstrap Confidence Interval Estimates with Censored and Truncated Data
http://digitalcommons.wayne.edu/jmasm/vol13/iss2/22
http://digitalcommons.wayne.edu/jmasm/vol13/iss2/22Tue, 09 Dec 2014 13:29:00 PST
Traditional inferential procedures often fail with censored and truncated data, especially when sample sizes are small. In this paper we evaluate the performances of the double and single bootstrap interval estimates by comparing the double percentile (DB-p), double percentile-t (DB-t), single percentile (B-p), and percentile-t (B-t) bootstrap interval estimation methods via a coverage probability study when the data is censored using the log logistic model. We then apply the double bootstrap intervals to real right censored lifetime data on 32 women with breast cancer and failure data on 98 brake pads where all the observations were left truncated.
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Jayanthi Arasan et al.Estimation of Multi Component Systems Reliability in Stress-Strength Models
http://digitalcommons.wayne.edu/jmasm/vol13/iss2/21
http://digitalcommons.wayne.edu/jmasm/vol13/iss2/21Tue, 09 Dec 2014 13:28:58 PST
In a system with standby redundancy, there are a number of components only one of which works at a time and the other remain as standbys. When an impact of stress exceeds the strength of the active component, for the first time, it fails and another from standbys, if there is any, is activated and faces the impact of stresses, not necessarily identical as faced by the preceding component and the system fails when all the components have failed. Sriwastav and Kakaty (1981) assumed that the components stress-strengths are similarly distributed. However, in general the stress distributions will be different from the strength distributions not only in parameter values but also in forms, because stresses are independent of strengths and the two are governed by different physical conditions. Assume the components in the system for both stress and strength are independent and follow different probability distributions viz. Exponential, Gamma, Lindley. Different conditions for stress and strength were considered. Under these assumptions the reliabilities of the system have been obtained with the help of the particular forms of density functions of n-standby system when all stress-strengths are random variables. The expressions for the marginal reliabilities R(1), R(2), R(3) etc. have been obtained based on its stress-strength models. Results obtained by J. Gogoi and M. Bohra are particular case presentations.
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Adil H. Khan et al.Reliability Estimates of Generalized Poisson Distribution and Generalized Geometric Series Distribution
http://digitalcommons.wayne.edu/jmasm/vol13/iss2/20
http://digitalcommons.wayne.edu/jmasm/vol13/iss2/20Tue, 09 Dec 2014 13:28:57 PST
Discrete distributions have played an important role in the reliability theory. In order to obtain Bayes estimators, researchers have adopted various conventional techniques. Generalizing the results of Maiti (1995), Chaturvadi and Tomer (2002) dealt with the problem of estimating P{X_{1}, X_{2}, …, X_{k} ≤ Y}, where random variables X and Y were assumed to follow a negative binomial distribution. Agit et al. obtained Bayesian estimates of the reliability functions and P{X_{1}, X_{2}, …, X_{k} ≤ Y} considering X and Y following binomial and Poisson distributions. The reliability function of the generalized Poisson and generalized geometric distribution is investigated. The expression for P{X_{1}, X_{2}, …, X_{k} ≤ Y} was obtained with X’s and Y following a Poisson distribution and some particular cases are shown.
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Adil H. Khan et al.Comparison of Individual and Moving Range Chart Combinations to Individual Charts in Terms of ARL after Designing for a Common “All OK” ARL
http://digitalcommons.wayne.edu/jmasm/vol13/iss2/19
http://digitalcommons.wayne.edu/jmasm/vol13/iss2/19Tue, 09 Dec 2014 13:28:56 PST
In some process monitoring situations, consecutive measurements are spaced widely apart in time, making monitoring process aim and spread difficult. This study uses three cases to compare the effectiveness of two such monitoring schemes, i.e., the X chart alone (X-only chart) and the Individuals and Moving Range Chart Combination (X/MR chars), in terms of Average Run Length (ARL) after designing for a common “all OK” (in-control) ARL. The study finds that X chart alone is sufficient (and hence, recommended) in detecting changes in all the 3 cases: changes in the process mean, changes in the process standard deviation, and changes in both process mean and standard deviation.
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Dewi RahardjaRidge Regression and Ill-Conditioning
http://digitalcommons.wayne.edu/jmasm/vol13/iss2/18
http://digitalcommons.wayne.edu/jmasm/vol13/iss2/18Tue, 09 Dec 2014 13:28:54 PST
Hoerl and Kennard (1970) suggested the ridge regression estimator as an alternative to the Ordinary Least Squares (OLS) estimator in the presence of multicollinearity. This article proposes new methods for estimating the ridge parameter in case of ordinary ridge regression. A simulation study evaluates the performance of the proposed estimators based on the Mean Squared Error (MSE) criterion and indicates that, under certain conditions, the proposed estimators perform well compared to the OLS estimator and another well-known estimator reviewed.
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Ghadban Khalaf et al.Some Methods of Estimation from Censored Samples in Exponential and Gamma Models
http://digitalcommons.wayne.edu/jmasm/vol13/iss2/17
http://digitalcommons.wayne.edu/jmasm/vol13/iss2/17Tue, 09 Dec 2014 13:28:53 PST
Two popular life testing models exponential and one where its generalization is gamma are considered. Estimation of scale parameter from a general Type-II doubly censored sample is attempted by the principle of maximum likelihood method. Resulting equations found to be giving iterative solutions. As an alternative to iterative solution certain admissible modifications to the estimating equations are suggested in special cases. The resulting estimates are compared with the exact maximum likelihood estimates analytically or through simulation. The results are also extended for reliability estimation.
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R R. L Kantam et al.Life Testing Analysis of Failure Censored Generalized Exponentiated Data
http://digitalcommons.wayne.edu/jmasm/vol13/iss2/16
http://digitalcommons.wayne.edu/jmasm/vol13/iss2/16Tue, 09 Dec 2014 13:28:52 PST
A generalized exponential distribution is considered for analyzing lifetime data; such statistical models are applicable when the observations are available in an ordered manner. This study examines failure censored data, which consist of testing n items and terminating the experiment when a pre-assigned number of items, for example r ( < n), have failed. Due to scale and shape parameters, both have flexibility for analyzing different types of lifetime data. This distribution has increasing, decreasing and a constant hazard rate depending on the shape parameter. This study provides maximum likelihood estimation and uniformly minimum variance unbiased techniques for the estimation of reliability of a component. Numerical computation was conducted on a data set and a comparison of the performance of two different techniques is presented.
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Anwar Hassan et al.