Statistics and Probability Commons^™

Regression Models For Mixed Over-Dispersed Poisson And Continuous Clustered Data: Modeling Bmi And Number Of Cigarettes Smoked Per Day, Folefac Atem, Julius S. Ngwa, Abidemi Adeniji

Journal of Modern Applied Statistical Methods

Clustered data, multiple observations collected on the same experimental unit, is common in epidemiological studies. Bivariate outcome data is often the result of interest in two correlated response variables. An efficient method is presented for dealing with bivariate outcomes when one outcome is continuous and the other is a count using a simple transformation to handle over-dispersed Poisson data. A multilevel analysis was performed on data from the National Health Interview Survey (NHIS) with body mass index (BMI) and the number of cigarettes smoked per day (NCS) as responses. Results show that these random effects models yield misleading results in …

Steady State Probabilities Of A Three Preemptive Single Server Queue, Ameen Jameel Alawneh

Journal of Modern Applied Statistical Methods

A three preemptive priority queuing system is considered where customers with three priorities joined a queue according to a Poisson process. A customer with higher priority needs to enter the service immediately upon arrival. The recursive formulas approach was extended to determine the steady state probabilities of such a priority queuing system.

Estimation Of Multinomial Proportions Using Higher Order Moments Of Scrambling Variables In Randomized Response Sampling, Cheng C. Chen, Sarjinder Singh

Journal of Modern Applied Statistical Methods

An extension to estimating multinomial proportions of potentially sensitive attributes in survey sampling is proposed using higher order moments of scrambling variables at the estimation stage to produce unbiased estimators. The variance and covariance expressions are derived and the relative efficiency of the proposed estimators based on scrambling variables is investigated.

Inverted Exponential Distribution Under A Bayesian Viewpoint, Gyan Prakash

Journal of Modern Applied Statistical Methods

The objective of this study was to examine the properties of Bayes estimators of the parameter, reliability function and hazard rate under the symmetric and asymmetric loss functions for the inverted exponential model. The Bayes predictive interval and the Bayes estimate of shift point are also determined. A simulation study was carried out to study the properties of the Bayes estimators.

Underlying Distributions In Loglinear Models Of Discrete Data, Tim Moses

Journal of Modern Applied Statistical Methods

The implications of loglinear models based on underlying uniform and binomial distribution are assessed with respect to modeling eight distributions. Regarding statistical selection of the loglinear models’ parameterizations, results indicate that better fitting models are obtained when the distribution being modeled is dissimilar to the underlying distribution used. For loglinear models with predetermined numbers of parameters, results suggest that better fitting models can be obtained when the distribution being modeled is similar to the underlying distribution.

Robust Modifications Of The Levene And O’Brien Tests For Spread, Abdul R. Othman, The Sin Yan, H. J. Keselman, Rand R. Wilcox, James Algina

Journal of Modern Applied Statistical Methods

Variants of Levene’s and O’Brien’s procedures not investigated by Keselman, Wilcox & Algina (2008) were examined. Simulations indicate that a new O’Brien variant provides very good Type I error control and is simpler for applied researchers to compute than the method recommended by Keselman, et al.

An Extension Of The Seasonal Kpss Test, Sami Khedhiri, Ghassen El Montasser

Journal of Modern Applied Statistical Methods

The limit theory of the seasonal KPSS test is established under the null hypothesis using seasonal dummy variables. Taking these variables into account can result in improved finite sample performance of the test. The seasonal KPSS test can be interpreted as a test of deterministic seasonality and it may be used in addition to seasonal unit root tests to analyze the dynamic properties of time series. The seasonal indicator variables provide the test with an explicit model-based regression that in itself constitutes a support for its limit theory.

Improved Estimator In The Presence Of Multicollinearity, Ghadban Khalaf

Journal of Modern Applied Statistical Methods

The performances of two biased estimators for the general linear regression model under conditions of collinearity are examined and a new proposed ridge parameter is introduced. Using Mean Square Error (MSE) and Monte Carlo simulation, the resulting estimator’s performance is evaluated and compared with the Ordinary Least Square (OLS) estimator and the Hoerl and Kennard (1970a) estimator. Results of the simulation study indicate that, with respect to MSE criteria, in all cases investigated the proposed estimator outperforms both the OLS and the Hoerl and Kennard estimators.

The Weighted Hellinger Distance For Kernel Distribution Estimator Of Function Of Observations, Abdel-Razzaq Mugdadi

Journal of Modern Applied Statistical Methods

The asymptotic mean weighted Hellinger distance (AMWHD) is derived for the kernel distribution estimator of a function of observations. In addition, the AMWHD is compared with the asymptotic mean integrated square error (AMISE) of the estimator. A completely data based method is proposed to select the bandwidth in the estimator using the mean weighted Hellinger distance (MWHD).

Planned Missingness Study Design: Two Methods To Developing The Study Survey Versions, E. Whitney G. Moore

Kinesiology, Health and Sport Studies

A planned missingness data study design takes advantage of modern techniques for handling data missingness that is MCAR (Missing Completely at Random) and MAR (Missing at Random) (Brown, 2006; Enders, 2010). As modern data imputation techniques have improved, this study design option has become a powerful, cost-effective option for collecting the most data across the largest sample possible, while keeping the fatigue effect and expense of the study minimized (Little, 2010a, 2010b, 2012). The purpose of this guide is to provide an applied example for designing the surveys necessary when conducting a planned missingness research study design.

Robustness And Power Of The Kornbrot Rank Difference, Signed Ranks, And Dependent Samples T-Test, Norman Haidous

Wayne State University Dissertations

ABSTRACT

ROBUSTNESS AND POWER OF THE KORNBROT RANK DIFFERENCE, SIGNED RANKS, AND DEPENDENT SAMPLES T-TEST

by

NORMAN N. HAIDOUS

December 2012

Advisor:Dr. Shlomo S. Sawilowsky

Major:Evaluation and Research - Statistics

Degree:Doctor of Philosophy

The purpose of the study was to compare the power and accuracy of the Wilcoxon Signed-Ranks test in comparison to the rank difference test when the assumption of normality is not met, the data are ordinal, and the sample size is small. The study also investigated Kornbrot's (1990) claim that the rank difference test should be used over the Wilcoxon Signed-Ranks tests "in all …

The Dependent Samples T And Wilcoxon Sign Rank Maximum Test, Saverpierre Maggio

Wayne State University Dissertations

A maximum test using the parametric dependent samples t-test and the non-parametric Wilcoxon sign rank test was created using a FORTRAN program and various subroutines of the International Mathematical and Statistical Libraries (IMSL, 1980). Two tailed critical values were derived from a mixed normal distribution. Critical values obtained were at the 0.05, 0.025, 0.01 and 0.005 alpha levels via sample sizes (n) 8 through 30, 45, 60, 90 and 120. Critical values were compared to values obtained through the application of the Bonferroni correction method. It was concluded that the Bonferroni is an unnecessary method. Findings of the study are …

Comparison Of Several Tests For Combining Several Independent Tests, Madhusudan Bhandary, Xuan Zhang

Journal of Modern Applied Statistical Methods

Several tests for combining p-values from independent tests have been considered to address a particular common testing problem. A simulation study shows that Fisher’s (1932) Inverse Chi-square test is optimal based on a power comparison of several different tests.

Discriminant Analysis For Repeated Measures Data: Effects Of Mean And Covariance Misspecification On Bias And Error In Discriminant Function Coefficients, Tolulope T. Sajobi, Lisa M. Lix, Longhai Li, William Laverty

Journal of Modern Applied Statistical Methods

Discriminant analysis (DA) procedures based on parsimonious mean and/or covariance structures have been proposed for repeated measures (RM) data. Bias and means square error of discriminant function coefficients (DFCs) for DA procedures are investigated when the mean and/or covariance structures are correctly specified and misspecified.

Construction Of Control Charts Based On Six Sigma Initiatives For The Number Of Defects And Average Number Of Defects Per Unit, R. Radhakrishnan, P. Balamurugan

Journal of Modern Applied Statistical Methods

A control chart is a statistical device used for the study and control of a repetitive process. In 1931, Shewart suggested control charts based on 3 sigma limits. Today manufacturing companies around the world apply Six Sigma initiatives, with a result offewer product defects. Companies practicing Six Sigma initiatives are expected to produce 3.4 or less number of defects per million opportunities, a concept suggested by Motorola in 1980. If companies practicing Six Sigma initiatives use control limits suggested by Shewhart, then no points will fall outside the control limits due to the improvement in the quality of the process. …

Identification Of Optimal Autoregressive Integrated Moving Average Model On Temperature Data, Olusola Samuel Makinde, Olusoga Akin Fasoranbaku

Journal of Modern Applied Statistical Methods

Autoregressive Integrated Moving Average (ARIMA) processes of various orders are presented to identify an optimal model from a class of models. Parameters of the models are estimated using an Ordinary Least Square (OLS) approach. ARIMA (p, d, q) is formulated for maximum daily temperature data in Ondo and Zaira from January 1995 to November 2005. The choice of ARIMA models of orders p and q is intended to retain persistence in a natural process. To determine the performance of models, Normalized Bayesian Information Criterion is adopted. The ARIMA (1, 1, 1) is adequate for modeling maximum daily temperature in Ondo …

Height-Diameter Relationship In Tree Modeling Using Simultaneous Equation Techniques In Correlated Normal Deviates, S. O. Oyamakin

Journal of Modern Applied Statistical Methods

In other to study the complex simultaneous relationships existing in forest/tree growth modeling, six estimation methods of a simultaneous equation model are examined to determine how they cope with varying degrees of correlation between pairs of random deviates using average parameter estimates. A two-equation simultaneous system assumed covariance matrix was considered. The model was structured to have a mutual correlation between pairs of random deviates: a violation of the assumption of mutual independence between pairs of such random deviates. The correlation between the pairs of normal deviates were generated using three scenarios r = 0.0, 0.3 and 0.5. The performances …

Tests For Correlation On Bivariate Non-Normal Data, L. Beversdorf, Ping Sa

Journal of Modern Applied Statistical Methods

Two statistics are considered to test the population correlation for non-normally distributed bivariate data. A simulation study shows that both statistics control type I error rates well for left-tailed tests and have reasonable power performance.

Lq-Moments For Regional Flood Frequency Analysis: A Case Study For The North-Bank Region Of The Brahmaputra River, India, Abhijit Bhuyan, Munindra Borah

Journal of Modern Applied Statistical Methods

The LQ-moment proposed by Mudholkar, et al. (1998) is used for regional flood frequency analysis of the North-Bank region of the river Brahmaputra, India. Five probability distributions are used for the LQmoment: generalized extreme value (GEV), generalized logistic (GLO) and generalized Pareto (GPA), lognormal (LN3) and Pearson Type III (PE3). The same regional frequency analysis procedure proposed by Hosking (1990) for the L-moment is used for the LQ-moment. Based on the LQ-moment ratio diagram and |Z_i^dist| -statistic criteria, the PE3 distribution is identified as the robust distribution for the study area. For estimation of floods of various …

Explicit Equations For Acf In Autoregressive Processes In The Presence Of Heteroscedasticity Disturbances, Samir Safi

Journal of Modern Applied Statistical Methods

The autocorrelation function, ACF, is an important guide to the properties of a time series. Explicit equations are derived for ACF in the presence of heteroscedasticity disturbances in pth order autoregressive, AR(p), processes. Two cases are presented: (1) when the disturbance term follows the general covariance matrix, Σ , and (2) when the diagonal elements of Σ are not all identical but σ_i,j = 0 ∀i ≠ j.

Type I Error Rates Of The Two-Sample Pseudo-Median Procedure, Nor Aishah Ahad, Abdul Rahman Othman, Sharipah Soaad Syed Yahaya

Journal of Modern Applied Statistical Methods

The performance of the pseudo-median based procedure is examined in terms of controlling Type I error for a two independent groups test. The procedure is a modification of the one-sample Wilcoxon statistic using the pseudo-median of differences between group values as the central measure of location. The proposed procedure was shown to have good control of Type I error rates under the study conditions regardless of distribution type.

Modified Ratio And Product Estimators For Population Mean In Systematic Sampling, Housila P. Singh, Rajesh Tailor, Narendra Kumar Jatwa

Journal of Modern Applied Statistical Methods

The estimation of population mean in systematic sampling is explored. Properties of a ratio and product estimator that have been suggested in systematic sampling are investigated, along with the properties of double sampling. Following Swain (1964), the cost aspect is also discussed.

Estimation Of Parameters Of Johnson’S System Of Distributions, Florence George, K. M. Ramachandran

Journal of Modern Applied Statistical Methods

Fitting distributions to data has a long history and many different procedures have been advocated. Although models like normal, log-normal and gamma lead to a wide variety of distribution shapes, they do not provide the degree of generality that is frequently desirable (Hahn & Shapiro, 1967). To formally represent a set of data by an empirical distribution, Johnson (1949) derived a system of curves with the flexibility to cover a wide variety of shapes. Methods available to estimate the parameters of the Johnson distribution are discussed, and a new approach to estimate the four parameters of the Johnson family is …

Robust Inference For Regression With Spatially Correlated Errors, Juchi Ou, Jeffrey M. Albert

Journal of Modern Applied Statistical Methods

A robust variance estimator for a regression model with spatially correlated errors is proposed using the estimated empirical covariogram. Simulations studies show unbiasedness and robustness for the OLS but not for the GLS estimates. The new robust variance estimation method is applied to hospital quality data.. Stephanie A.

Maximum Log Likelihood Estimation Using Em Algorithm And Partition Maximum Log Likelihood Estimation For Mixtures Of Generalized Lambda Distributions, Steve Su

Journal of Modern Applied Statistical Methods

Two mixture distribution fitting methods based on maximizing the likelihood using generalized lambda distributions are presented. The fitting algorithms are demonstrated on various data and the strengths and weakness of the algorithms which can influence their use under different mixture modeling situations are discussed. The procedures described are available in GLDEX package in R.

A Sequential Monte Carlo Approach For Online Stock Market Prediction Using Hidden Markov Models, Ahani E. Bridget, O. Abass

Journal of Modern Applied Statistical Methods

A sequential Monte Carlo (SMC) algorithm prediction approach is developed based on joint probability distribution in hidden Markov Models (HMM). SMC methods, a general class of Monte Carlo methods, are typically used for sampling from sequences of distributions and simple examples of these algorithms are found extensively throughout the tracking and signal processing literature. Recent developments indicate that these techniques have much more general applicability and can be applied very effectively to statistical inference problems. Due to the problem involved in estimating the parameter of HMM, the HMM is represented in a state space model and the sequential Monte Carlo …

Jmasm31: Manova Procedure For Power Calculations (Spss), Alan Taylor

Journal of Modern Applied Statistical Methods

D’Amico, Neilands & Zambarano (2001) showed how the SPSS MANOVA procedure can be used to conduct power calculations for research designs. This article demonstrates a simple way of entering data required for power calculations into SPSS and provides examples that supplement those given by D’Amico, Neilands & Zambarano.

A Pooled Two-Sample Median Test Based On Density Estimation, Vadim Y. Bichutskiy

Journal of Modern Applied Statistical Methods

A new method based on density estimation is proposed for medians of two independent samples. The test controls the probability of Type I error and is at least as powerful as methods widely used in statistical practice. The method can be implemented using existing libraries in R.

Higher Order Markov Structure-Based Logistic Model And Likelihood Inference For Ordinal Data, Soma Chowdhury Biswas, M. Ataharul Islam, Jamal Nazrul Islam

Journal of Modern Applied Statistical Methods

Azzalini (1994) proposed a first order Markov chain for binary data. Azzalini’s model is extended for ordinal data and introduces a second order model. Further, the test statistics are developed and the power of the test is determined. An application using real data is also presented.

Robustness, Power And Interpretability Of Pairwise Tests Of Discriminant Functions In Manova, Philip H. Ramsey, Patricia P. Ramsey, Priscila Hachimine, Nancy Andiloro

Journal of Modern Applied Statistical Methods

Limiting follow-up hypotheses to be tested can reduce problems relating to the control of Type I and Type II errors in multivariate analysis of variance (MANOVA). Such limitations can also improve the interpretability of results. The importance of sample size, shape of population distribution, within-group correlations and heterogeneity of variances are demonstrated. The protected greatest characteristic root (GCR) procedure is shown to work well for small, group size, N (≤ 10). The unprotected GCR is shown to work well for larger N.