Open Journal of Statistics
http://www.i-scholar.in/index.php/OJS
<p>Open Journal of Statistics (OJS) is an international journal dedicated to the latest advancements in statistics. The goal of this journal is to provide a platform for scientists and academicians all over the world to promote, share, and discuss various new issues and developments in different areas of statistics.</p>en-USjournals@scirp.org (Prof.Qihua Wang)journals@scirp.org (Mr. Danling Wang)Fri, 15 Apr 2016 10:46:47 +0000OJS 2.4.2.0http://blogs.law.harvard.edu/tech/rss60A Modified Epidemic Chain Binomial Model
http://www.i-scholar.in/index.php/OJS/article/view/96061
Discrete epidemic models are applied to describe the physical phenomena of spreading infectious diseases in a household. In this paper, an attempt has been made to develop a modified epidemic chain model by assuming a beta distribution of third kind for the probability of being infected by contact with a given infective from the same household with closed population. This paper emphasizes mainly on developing the probabilities of all possible epidemic chains with one introductory case for three, four and five member household. The key phenomenon towards developing this paper is to provide an alternative model of chain binomial model.Dilip C. Nath, Kishore K. Das, Tandrima Chakrabortyhttp://www.i-scholar.in/index.php/OJS/article/view/96061Mon, 01 Feb 2016 00:00:00 +0000Comparison of Cost Incurred in Two Survey Methodologies for Measles Vaccine Coverage
http://www.i-scholar.in/index.php/OJS/article/view/96063
Background: The World Health Organization (WHO) initiated the Expanded Program on Immunization (EPI) in 1974. It has been widely used in different studies. Along with this, other survey methodologies have been compared to study immunization coverage at different regions. To consider different survey methodologies, one of the most important factors is the cost incurred that survey methodology. A survey method is considered as more efficient or better than the other survey method if the cost incurred in a particular method is less than the other one. Methods: In this study, cost incurred in two stage (30 × 30) cluster sampling and systematic sampling methods have been compared using a cost function for measles vaccine coverage. Measles vaccine coverage data has been taken from the survey "Comparison of Two Survey Methodologies to Estimates Total Vaccination Coverage" sponsored by Indian Council of Medical Research (ICMR), New Delhi. Results: The results show that there are no significant differences between the point estimates of measles vaccine coverage under the considered survey methodologies. But the cost incurred in systematic sampling is more than that of two stage cluster sampling. Conclusion: It can be concluded that systematic sampling survey is costlier than that of two stage cluster sampling for this study population.Dilip C. Nath, Bhushita Patowarihttp://www.i-scholar.in/index.php/OJS/article/view/96063Mon, 01 Feb 2016 00:00:00 +0000Hypothesis Testing of Population Percentiles via the Wald Test with Bootstrap Variance Estimates
http://www.i-scholar.in/index.php/OJS/article/view/96067
Testing the equality of percentiles (quantiles) between populations is an effective method for robust, nonparametric comparison, especially when the distributions are asymmetric or irregularly shaped. Unlike global nonparametric tests for homogeneity such as the Kolmogorv-Smirnov test, testing the equality of a set of percentiles (i.e., a <em>percentile profile</em>) yields an estimate of the location and extent of the differences between the populations along the entire domain. The Wald test using bootstrap estimates of variance of the order statistics provides a unified method for hypothesis testing of functions of the population percentiles. Simulation studies are conducted to show performance of the method under various scenarios and to give suggestions on its use. Several examples are given to illustrate some useful applications to real data.William D. Johnson, Jacob E. Romerhttp://www.i-scholar.in/index.php/OJS/article/view/96067Mon, 01 Feb 2016 00:00:00 +0000Piketty's Capital-Income Theory Reconsidered for a Small Open Economy with Increasing Savings Rate
http://www.i-scholar.in/index.php/OJS/article/view/96068
Since Piketty offered a new view of capital/income ratio, numerous attempts have been made to examine the relationship between return on capital, economic growth and the capital/income ratio. This paper attempts to shed new light on this field. More precisely, following recent literatures that pay attention to dynamics of external balance sheets of countries, we examine if Piketty's results for large countries are robust for a country that takes the world rate of return on capital as given and whose savings rate increases gradually from negative value. It is revealed that for such a country, (1) Kuznets curve is drawn and (2) capital/income ratio decreases in accordance with a rise in savings rate and return on capital.Yasunori Fujitahttp://www.i-scholar.in/index.php/OJS/article/view/96068Mon, 01 Feb 2016 00:00:00 +0000A New Definition of Intuitionistic Fuzzy Similarity Degree
http://www.i-scholar.in/index.php/OJS/article/view/96071
As far as the problem of intuitionistic fuzzy cluster analysis is concerned, this paper proposes a new formula of similarity degree with attribute weight of each index. We conduct a fuzzy cluster analysis based on the new intuitionistic fuzzy similarity matrix, which is constructed via this new weighted similarity degree method and can be transformed into a fuzzy similarity matrix. Moreover, an example is given to demonstrate the feasibility and validity of this method.Qun Liu, Changhuan Fenghttp://www.i-scholar.in/index.php/OJS/article/view/96071Mon, 01 Feb 2016 00:00:00 +0000Some Construction Methods of Optimum Chemical Balance Weighing Designs III
http://www.i-scholar.in/index.php/OJS/article/view/96074
Methods of constructing the optimum chemical balance weighing designs from symmetric balanced incomplete block designs are proposed with illustration. As a by-product pairwise efficiency and variance balanced designs are also obtained.Rashmi Awad, Shakti Banerjeehttp://www.i-scholar.in/index.php/OJS/article/view/96074Mon, 01 Feb 2016 00:00:00 +0000Bayesian Estimation and Prediction for the Maxwell Failure Distribution based on Type II Censored Data
http://www.i-scholar.in/index.php/OJS/article/view/96078
We present Bayes estimators, highest posterior density (HPD) intervals, and maximum likelihood estimators (MLEs), for the Maxwell failure distribution based on Type II censored data, i.e. using the first r lifetimes from a group of n components under test. Reliability/Hazard function estimates, Bayes predictive distributions and highest posterior density prediction intervals for a future observation are also considered. Two data examples and a Monte Carlo simulation study are used to illustrate the results and to compare the performances of the different methods.Anwar M. Hossain, Gabriel Huertahttp://www.i-scholar.in/index.php/OJS/article/view/96078Mon, 01 Feb 2016 00:00:00 +0000Estimation of Regression Function for Nonequispaced Samples based on Warped Wavelets
http://www.i-scholar.in/index.php/OJS/article/view/96080
We consider the problem of estimating an unknown density and its derivatives in a regression setting with random design. Instead of expanding the function on a regular wavelet basis, we expand it on the basis φ (G(x)) , a warped wavelet basis. We investigate the properties of this new basis and evaluate its asymptotic performance by determining an upper bound of the mean integrated squared error under different dependence structures. We prove that it attains a sharp rate of convergence for a wide class of unknown regression functions.Nargess Hosseiniounhttp://www.i-scholar.in/index.php/OJS/article/view/96080Mon, 01 Feb 2016 00:00:00 +0000An Alternative Approach to AIC and Mallow's Cp Statistic-Based Relative Influence Measures (RIMS) in Regression Variable Selection
http://www.i-scholar.in/index.php/OJS/article/view/96083
Outlier detection is an important data screening type. RIM is a mechanism of outlier detection that identifies the contribution of data points in a regression model. A BIC-based RIM is essentially a technique developed in this work to simultaneously detect influential data points and select optimal predictor variables. It is an addition to the body of existing literature in this area of study to both having an alternative to the AIC and Mallow's C<sub>p</sub> Statistic-based RIM as well as conditions of no influence, some sort of influence and perfectly single outlier data point in an entire data set which are proposed in this work. The method is implemented in R by an algorithm that iterates over all data points; deleting data points one at a time while computing BICs and selecting optimal predictors alongside RIMs. From the analyses done using evaporation data to compare the proposed method and the existing methods, the results show that the same data cases selected as having high influences by the two existing methods are also selected by the proposed method. The three methods show same performance; hence the relevance of the BIC-based RIM cannot be undermined. to the AIC and MalloUmeh Edith Uzoma, Obulezi Okechukwu Jeremiahhttp://www.i-scholar.in/index.php/OJS/article/view/96083Mon, 01 Feb 2016 00:00:00 +0000Local Curvature and Centering Effects in Nonlinear Regression Models
http://www.i-scholar.in/index.php/OJS/article/view/96086
The effects of centering response and explanatory variables as a way of simplifying fitted linear models in the presence of correlation are reviewed and extended to include nonlinear models, common in many biological and economic applications. In a nonlinear model, the use of a local approximation can modify the effect of centering. Even in the presence of uncorrelated explanatory variables, centering may affect linear approximations and related test statistics. An approach to assessing this effect in relation to intrinsic curvature is developed and applied. Mis-specification bias of linear versus nonlinear models also reflects this centering effect.Michael Brimacombehttp://www.i-scholar.in/index.php/OJS/article/view/96086Mon, 01 Feb 2016 00:00:00 +0000Improved Estimation of Rare Sensitive Attribute in a Stratified Sampling using Poisson Distribution
http://www.i-scholar.in/index.php/OJS/article/view/96089
In this study, we propose a two stage randomized response model. Improved unbiased estimators of the mean number of persons possessing a rare sensitive attribute under two different situations are proposed. The proposed estimators are evaluated using a relative efficiency comparison. It is shown that our estimators are efficient as compared to existing estimators when the parameter of rare unrelated attribute is known and in unknown case, depending on the probability of selecting a question.Abdul Wakeel, Masood Anwarhttp://www.i-scholar.in/index.php/OJS/article/view/96089Mon, 01 Feb 2016 00:00:00 +0000On the Performances of Classical VAR and Sims-Zha Bayesian VAR Models in the Presence of Collinearity and Autocorrelated Error Terms
http://www.i-scholar.in/index.php/OJS/article/view/96093
In time series literature, many authors have found out that multicollinearity and autocorrelation usually afflict time series data. In this paper, we compare the performances of classical VAR and Sims-Zha Bayesian VAR models with quadratic decay on bivariate time series data jointly influenced by collinearity and autocorrelation. We simulate bivariate time series data for different collinearity levels (−0.99, −0.95, −0.9, −0.85, −0.8, 0.8, 0.85, 0.9, 0.95, 0.99) and autocorrelation levels (−0.99, −0.95, −0.9, −0.85, −0.8, 0.8, 0.85, 0.9, 0.95, 0.99) for time series length of 8, 16, 32, 64, 128, 256 respectively. The results from 10,000 simulations reveal that the models performance varies with the collinearity and autocorrelation levels, and with the time series lengths. In addition, the results reveal that the BVAR4 model is a viable model for forecasting. Therefore, we recommend that the levels of collinearity and autocorrelation, and the time series length should be considered in using an appropriate model for forecasting.M. O. Adenomon, V. A. Michael, O. P. Evanshttp://www.i-scholar.in/index.php/OJS/article/view/96093Mon, 01 Feb 2016 00:00:00 +0000Transformation Models for Survival Data Analysis with Applications
http://www.i-scholar.in/index.php/OJS/article/view/96095
When the event of interest never occurs for a proportion of subjects during the study period, survival models with a cure fraction are more appropriate in analyzing this type of data. Considering the non-linear relationship between response variable and covariates, we propose a class of generalized transformation models motivated by Zeng et al. [1] transformed proportional time cure model, in which fractional polynomials are used instead of the simple linear combination of the covariates. Statistical properties of the proposed models are investigated, including identifiability of the parameters, asymptotic consistency, and asymptotic normality of the estimated regression coefficients. A simulation study is carried out to examine the performance of the power selection procedure. The generalized transformation cure rate models are applied to the First National Health and Nutrition Examination Survey Epidemiologic Follow-up Study (NHANES1) for the purpose of examining the relationship between survival time of patients and several risk factors.Yang Liu, Qiusheng Chen, Xufeng Niuhttp://www.i-scholar.in/index.php/OJS/article/view/96095Mon, 01 Feb 2016 00:00:00 +0000Student’s t Increments
http://www.i-scholar.in/index.php/OJS/article/view/96097
Some moments and limiting properties of independent Student's t increments are studied. Independent Student's t increments are independent draws from not-truncated, truncated, and effectively truncated Student's t-distributions with shape parameters ν ≥ 1 and can be used to create random walks. It is found that sample paths created from truncated and effectively truncated Student's t-distributions are continuous. Sample paths for ν ≥ 3 Student's t-distributions are also continuous. Student's t increments should thus be useful in construction of stochastic processes and as noise driving terms in Langevin equations.Daniel T. Cassidyhttp://www.i-scholar.in/index.php/OJS/article/view/96097Mon, 01 Feb 2016 00:00:00 +0000A Comparison of Two Linear Discriminant Analysis Methods That Use Block Monotone Missing Training Data
http://www.i-scholar.in/index.php/OJS/article/view/96100
We revisit a comparison of two discriminant analysis procedures, namely the linear combination classifier of Chung and Han (2000) and the maximum likelihood estimation substitution classifier for the problem of classifying unlabeled multivariate normal observations with equal covariance matrices into one of two classes. Both classes have matching block monotone missing training data. Here, we demonstrate that for intra-class covariance structures with at least small correlation among the variables with missing data and the variables without block missing data, the maximum likelihood estimation substitution classifier outperforms the Chung and Han (2000) classifier regardless of the percent of missing observations. Specifically, we examine the differences in the estimated expected error rates for these classifiers using a Monte Carlo simulation, and we compare the two classifiers using two real data sets with monotone missing data via parametric bootstrap simulations. Our results contradict the conclusions of Chung and Han (2000) that their linear combination classifier is superior to the MLE classifier for block monotone missing multivariate normal data.Phil D. Young, Dean M. Young, Songthip T. Ounpraseuthhttp://www.i-scholar.in/index.php/OJS/article/view/96100Mon, 01 Feb 2016 00:00:00 +0000The Dual of the Maximum Likelihood Method
http://www.i-scholar.in/index.php/OJS/article/view/96102
The Maximum Likelihood method estimates the parameter values of a statistical model that maximizes the corresponding likelihood function, given the sample information. This is the primal approach that, in this paper, is presented as a mathematical programming specification whose solution requires the formulation of a Lagrange problem. A result of this setup is that the Lagrange multipliers associated with the linear statistical model (where sample observations are regarded as a set of constraints) are equal to the vector of residuals scaled by the variance of those residuals. The novel contribution of this paper consists in deriving the dual model of the Maximum Likelihood method under normality assumptions. This model minimizes a function of the variance of the error terms subject to orthogonality conditions between the model residuals and the space of explanatory variables. An intuitive interpretation of the dual problem appeals to basic elements of information theory and an economic interpretation of Lagrange multipliers to establish that the dual maximizes the net value of the sample information. This paper presents the dual ML model for a single regression and provides a numerical example of how to obtain maximum likelihood estimates of the parameters of a linear statistical model using the dual specification.Quirino Parishttp://www.i-scholar.in/index.php/OJS/article/view/96102Mon, 01 Feb 2016 00:00:00 +0000Predictive Modeling of Gas Production, Utilization and Flaring in Nigeria using <i>TSRM</i> and <i>TSNN</i>: A Comparative Approach
http://www.i-scholar.in/index.php/OJS/article/view/96105
Since the discovery of oil and gas in Nigeria in 1956, much gas has been flared because the operators pay little or no concern to its utilization, and as such, trillions of dollars have been lost. In this paper, a model is proposed using <em>Time Series Regression Model (TSRM) and Time Series Neural Network (TSNN)</em> to model the production, utilization and flaring of natural gas in Nigeria with the ultimate aim of observing the trend of each activity. The results show that <em>TSNN</em> has better predictive and forecasting capabilities compared to <em>TSRN</em>. It is also observed that the higher the hidden neurons, the lower the error generated by the <em>TSNN</em>.Olugbenga Falode, Christopher Udombosohttp://www.i-scholar.in/index.php/OJS/article/view/96105Mon, 01 Feb 2016 00:00:00 +0000