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Articles 1 - 30 of 73
Full-Text Articles in Statistics and Probability
On The Distribution Of Quadratic Expressions In Various Types Of Random Vectors, Ali Akbar Mohsenipour
On The Distribution Of Quadratic Expressions In Various Types Of Random Vectors, Ali Akbar Mohsenipour
Electronic Thesis and Dissertation Repository
Several approximations to the distribution of indefinite quadratic expressions in possibly singular Gaussian random vectors and ratios thereof are obtained in this dissertation. It is established that such quadratic expressions can be represented in their most general form as the difference of two positive definite quadratic forms plus a linear combination of Gaussian random variables. New advances on the distribution of quadratic expressions in elliptically contoured vectors, which are expressed as scalar mixtures of Gaussian vectors, are proposed as well. Certain distributional aspects of Hermitian quadratic expressions in complex Gaussian vectors are also investigated. Additionally, approximations to the distributions of …
Selection Of Mixed Sampling Plan With Qss-1(N; CN, CT) Plan As Attribute Plan Indexed Through Mapd And Lql, R. Sampath Kumar, M. Indra, R. Radhakrishnan
Selection Of Mixed Sampling Plan With Qss-1(N; CN, CT) Plan As Attribute Plan Indexed Through Mapd And Lql, R. Sampath Kumar, M. Indra, R. Radhakrishnan
Journal of Modern Applied Statistical Methods
A procedure for the construction and selection of the mixed sampling plan using MAPD as a quality standard with the QSS-1 (n; cN, cT) plan as an attribute plan is presented. The plans indexed through MAPD and LQL are constructed and compared for efficiency. Tables are provided for selection of an appropriate sampling plan.
Regression Split By Levels Of The Dependent Variable, Stan Lipovetsky
Regression Split By Levels Of The Dependent Variable, Stan Lipovetsky
Journal of Modern Applied Statistical Methods
Multiple regression coefficients split by the levels of the dependent variable are examined. The decomposition of the coefficients can be defined by points on the ordinal scale or by levels in the numerical response using the Gifi system of binary variables. This approach permits consideration of specific values of the coefficients at each layer of the response variable. Numerical results illustrate how to identify levels of interpretable regression coefficients.
Class(Es) Of Factor-Type Estimator(S) In Presence Of Measurement Error, Diwakar Shukla, Sharad Pathak, Narendra Singh Thakur
Class(Es) Of Factor-Type Estimator(S) In Presence Of Measurement Error, Diwakar Shukla, Sharad Pathak, Narendra Singh Thakur
Journal of Modern Applied Statistical Methods
When data is collected via sample survey it is assumed whatever is reported by a respondent is correct. However, given the issues of prestige bias, personal respect and honor, respondents’ self-reported data often produces over- or under- estimated values as opposed to true values regarding the variables under question. This causes measurement error to be present in sample values. This article considers the factortype estimator as an estimation tool and examines its performance under a measurement error model. Expressions of optimization are derived and theoretical results are supported by numerical examples.
A Graphical Examination Of Variable Deletion Within The Mewma Statistic, Jay R. Schaffer, Shawn Vandenhul
A Graphical Examination Of Variable Deletion Within The Mewma Statistic, Jay R. Schaffer, Shawn Vandenhul
Journal of Modern Applied Statistical Methods
A general procedure for identifying the variable(s) that contribute(s) to the signal of the multivariate extension of the exponentially weighted moving average (MEWMA) chart is presented. The procedure systematically removes one or two variables from the MEWMA statistic calculations. Percentages are calculated for correctly identifying various shifts.
Examining Multiple Comparison Procedures According To Error Rate, Power Type And False Discovery Rate, Guven Ozkaya, Ilker Ercan
Examining Multiple Comparison Procedures According To Error Rate, Power Type And False Discovery Rate, Guven Ozkaya, Ilker Ercan
Journal of Modern Applied Statistical Methods
Examining pairwise differences between means is a common practice of applied researchers, and the selection of an appropriate multiple comparison procedure (MCP) is important for analyzing pairwise comparisons. This study examines the performance of MCPs under the assumption of homogeneity of variances for various numbers of groups with equal and unequal sample sizes via a simulation study. MCPs are compared according to type I error rate, power type and false discovery rate (FDR). Results show that the LSD and Duncan procedures have high error rates and Scheffe’s procedure has low power; no remarkable differences between the other procedures considered were …
Modified Edf Goodness Of Fit Tests For Logistic Distribution Under Srs And Rss, S. A. Al-Subh, M. T. Alodat, Kamaruzaman Ibrahim, Abdul Aziz Jemain
Modified Edf Goodness Of Fit Tests For Logistic Distribution Under Srs And Rss, S. A. Al-Subh, M. T. Alodat, Kamaruzaman Ibrahim, Abdul Aziz Jemain
Journal of Modern Applied Statistical Methods
Modified forms of goodness of fit tests are presented for the logistic distribution using statistics based on the empirical distribution function (EDF). A method to improve the power of the modified EDF goodness of fit tests is introduced based on Ranked Set sampling (RSS). Data are collected via the Ranked Set Sampling (RSS) technique (McIntyre, 1952). Critical values for the logistic distribution with unknown parameters are provided and the powers of the tests are given for a number of alternative distributions. A simulation study is presented to illustrate the power of the new method.
On Some Negative Integer Moments Of Quasi-Negative-Binomial Distribution, Anwar Hassan, Sheikh Bilal
On Some Negative Integer Moments Of Quasi-Negative-Binomial Distribution, Anwar Hassan, Sheikh Bilal
Journal of Modern Applied Statistical Methods
Negative integer moments of the quasi-negative-binomial distribution (QNBD) are investigated. This distribution includes recurrence relations which are helpful in the solution of many applied statistical problems, particularly in life testing and survey sampling, where ratio estimators are useful. Results study show the negative-binomial distribution when the parameter θ2 is zero and also indicate the mean of the QNBD model when its parameters are changed.
Single Sampling Plans For Variables Indexed By Aql And Aoql With Measurement Error, R. Sankle, J.R. Singh
Single Sampling Plans For Variables Indexed By Aql And Aoql With Measurement Error, R. Sankle, J.R. Singh
Journal of Modern Applied Statistical Methods
Single sampling plans are investigated for variables indexed by acceptable quality level (AQL) and average outgoing quality limit (AOQL) under measurement error. Procedures and tables are provided for selection of single sampling plans for variables for given AQL and AOQL when rejected lots are 100% inspected for replacement of a nonconforming unit. For a particular sampling plan in operation for an observed measurement, a method for determining true operating characteristic (OC) functions and average outgoing quality (AOQ) is described for various error sizes.
Small-To-Medium Enterprises And Economic Growth: A Comparative Study Of Clustering Techniques, Karim K. Mardaneh
Small-To-Medium Enterprises And Economic Growth: A Comparative Study Of Clustering Techniques, Karim K. Mardaneh
Journal of Modern Applied Statistical Methods
Small-to-medium enterprises (SMEs) in regional (non-metropolitan) areas are considered when economic planning may require large data sets and sophisticated clustering techniques. The economic growth of regional areas was investigated using four clustering algorithms. Empirical analysis demonstrated that the modified global k-means algorithm outperformed other algorithms.
Exact Logistic Regression For A Matched Pairs Case-Control Design With Polytomous Exposure Variables, Shyam S. Ganguly
Exact Logistic Regression For A Matched Pairs Case-Control Design With Polytomous Exposure Variables, Shyam S. Ganguly
Journal of Modern Applied Statistical Methods
Logistic regression methods are useful in estimating odds ratios under matched pairs case-control designs when the exposure variable of interest is binary or polytomous in nature. Analysis is typically performed using large sample approximation techniques. When conducting the analysis with polytomous exposure variable, situations where the numbers of discordant pairs in the resulting cells are small or the data structure is sparse can be encountered. In such situations, the asymptotic method of analysis is questionable, thus an exact method of analysis may be more suitable. A method is presented that performs exact inference in the case of pair-wise matched case-control …
Graphical Modeling For High Dimensional Data, Munni Begum, Jay Bagga, C. Ann Blakey
Graphical Modeling For High Dimensional Data, Munni Begum, Jay Bagga, C. Ann Blakey
Journal of Modern Applied Statistical Methods
With advances in science and information technologies, many scientific fields are able to meet the challenges of managing and analyzing high-dimensional data. A so-called large p small n problem arises when the number of experimental units, n, is equal to or smaller than the number of features, p. A methodology based on probability and graph theory, termed graphical models, is applied to study the structure and inference of such high-dimensional data.
Extreme Value Charts And Analysis Of Means (Anom) Based On The Log Logistic Distribution, B. Srinivasa Rao, J. Pratapa Reddy, G. Sarath Babu
Extreme Value Charts And Analysis Of Means (Anom) Based On The Log Logistic Distribution, B. Srinivasa Rao, J. Pratapa Reddy, G. Sarath Babu
Journal of Modern Applied Statistical Methods
A probability model of a quality characteristic is assumed to follow a log logistic distribution. This article proposes variable control charts, termed extreme value charts, based on the extreme values of each subgroup. The control chart constants depend on the probability model of the extreme order statistics and the size of each subgroup. The analysis of means (ANOM) technique for a skewed population is applied with respect to log logistic distribution. Results are illustrated using examples based on real data.
Weighted Cook-Johnson Copula And Their Characterizations: Application To Probably Modeling Of The Hot Spring Eruptions, Hakim Bekrizadeh, Gholam Ali Parham, Mohamd Reza Zadkarmi
Weighted Cook-Johnson Copula And Their Characterizations: Application To Probably Modeling Of The Hot Spring Eruptions, Hakim Bekrizadeh, Gholam Ali Parham, Mohamd Reza Zadkarmi
Journal of Modern Applied Statistical Methods
Copulas have emerged as a practical method for multivariate modeling. A limited amount of work has been conducted regarding the application of copula-based modeling in context analysis. This study generalizes the Cook-Johnson copula under the appropriate weighted function and provides examples and the properties of the generalized Cook-Johnson copula. Results show that the generalized Cook-Johnson copula is suitable for probable modeling of hot spring eruption.
Examining Growth With Statistical Shape Analysis And Comparison Of Growth Models, Deniz Sigirli, Ilker Ercan
Examining Growth With Statistical Shape Analysis And Comparison Of Growth Models, Deniz Sigirli, Ilker Ercan
Journal of Modern Applied Statistical Methods
Growth curves have been widely used in the fields of biology, zoology and medicine for assessing some measurable trait of an organism, such as height, weight, area or volume. In statistical shape analysis, a size measure is obtained using the geometrical information of an object as opposed to linear measurements. The performances of commonly used non-linear growth curves are compared by using centroid size as a size measure in a simulation study. An example is provided on the relationship between centroid size of the cerebellum and disease duration in multiple sclerosis patients.
Posterior Estimates Of Poisson Distribution Using R Software, Raja Sultan, S.P. Ahmad
Posterior Estimates Of Poisson Distribution Using R Software, Raja Sultan, S.P. Ahmad
Journal of Modern Applied Statistical Methods
The Bayesian estimation of unknown parameter of the Poisson distribution is examined under different priors. The posterior distributions for the unknown parameter of the Poisson distribution are derived using the following priors: uniform, Jeffrey’s, Gamma distribution, Gamma-Chi-square distribution, Gammaexponential distribution and Chi-square-exponential distribution. Numerical and graphical illustrations of the posterior densities of the parameters of interest were conducted using R Software.
Ferrieri's Index Of Openness Applied To Remittances To Developing Countries, Gaetano Ferrieri
Ferrieri's Index Of Openness Applied To Remittances To Developing Countries, Gaetano Ferrieri
Journal of Modern Applied Statistical Methods
A new methodology to measure international openness and globalization is described. This allows capacity to be effectively combined with size in a number of socio-economic areas, such as trade, migration and foreign investment. The method is applied to remittances to developing countries.
Multivariate Generalized Poisson Distribution For Interference On Selected Non-Communicable Diseases In Lagos State, Nigeria, Adewara Johnson Ademola, Mbata Ugochuckwu Ahamefula
Multivariate Generalized Poisson Distribution For Interference On Selected Non-Communicable Diseases In Lagos State, Nigeria, Adewara Johnson Ademola, Mbata Ugochuckwu Ahamefula
Journal of Modern Applied Statistical Methods
Multivariate Generalized Poisson Distribution (MGPD) models are applied to make inferences regarding non-communicable diseases, diabetes, hypertension, stroke and ulcer in Lagos State, Nigeria. The generalized Poisson distribution is employed due to its usefulness in modeling count data in the presence of either over- or under- dispersion. Results show that the correlation between ulcer and stroke is not significant. Other pairwise comparisons of diseases are significant, thus implying that a patient who suffers from diabetes or stroke has a high propensity to also be hypertensive.
Comparing Two Independent Groups Via A Quantile Generalization Of The Wilcoxon-Mann-Whitney Test, Rand R. Wilcox
Comparing Two Independent Groups Via A Quantile Generalization Of The Wilcoxon-Mann-Whitney Test, Rand R. Wilcox
Journal of Modern Applied Statistical Methods
The Wilcoxon-Mann-Whitney test, as well as modern improvements, are based in part on an estimate of p = P(D < 0), where D = X−Y and X and Y are independent random variables; a common goal is to test H0: p = 0.5. This corresponds to testing H0: ξ0.5, where ξ0.5 is the 0.5 quantile of the distribution of D. If the distributions associated with X and Y do not differ, then D has a symmetric distribution about zero. In particular, ξq + ξ1-q = 0 for any q ≤ 0.5, where ξq is the qth quantile. Methods aimed at testing H0: p = 0.5 are generalized by …
Testing The Population Coefficient Of Variation, Shipra Banik, B. M. Golam Kibria, Dinesh Sharma
Testing The Population Coefficient Of Variation, Shipra Banik, B. M. Golam Kibria, Dinesh Sharma
Journal of Modern Applied Statistical Methods
The coefficient of variation (CV), which is used in many scientific areas, measures the variability of a population relative to its mean and standard deviation. Several methods exist for testing the population CV. This article compares a proposed bootstrap method to existing methods. A simulation study was conducted under both symmetric and skewed distributions to compare the performance of test statistics with respect to empirical size and power. Results indicate that some of the proposed methods are useful and can be recommended to practitioners.
On Some Properties And Estimation Of Size-Biased Polya-Eggenberger Distribution, Anwar Hassan, Sheikh Bilal, Imtiyaz Ahmad Shah
On Some Properties And Estimation Of Size-Biased Polya-Eggenberger Distribution, Anwar Hassan, Sheikh Bilal, Imtiyaz Ahmad Shah
Journal of Modern Applied Statistical Methods
A size-biased version of Polya-Eggenberger distribution is introduced explicitly and by a mixture model. The proposed distribution is unimodal with positive integer moments. The recurrence relation between moments (about the origin) of the proposed distribution is established and its relationship with other distributions is discussed. Different estimation techniques are proposed to estimate the parameters of the distribution.
An Extension Of Cochran-Orcutt Procedure For Generalized Linear Regression Models With Periodically Correlated Errors, Abdullah A. Smadi, Nour H. Abu-Afouna
An Extension Of Cochran-Orcutt Procedure For Generalized Linear Regression Models With Periodically Correlated Errors, Abdullah A. Smadi, Nour H. Abu-Afouna
Journal of Modern Applied Statistical Methods
An important assumption of ordinary regression models is independence among errors. This research considers the case of periodically correlated errors following the periodic AR model of order 1 (PAR(1)). The remedial measure for correlated errors in regression known as the Cochran-Orcutt procedure is generalized to the case of periodically correlated errors. The motivation for making such generalizations is that the response data may inhibit some seasonality, which may not be captured by the traditional AR(1) autoregressive model. The proposed procedure is described and the bias and MSE of the resulting intercept and slope parameter estimates of the simple LR model …
Bayesian Estimation Of Erlang Distribution Under Different Generalized Truncated Distributions As Priors, Adil H. Khan, T.R. Jan
Bayesian Estimation Of Erlang Distribution Under Different Generalized Truncated Distributions As Priors, Adil H. Khan, T.R. Jan
Journal of Modern Applied Statistical Methods
Various generalized truncated distributions are considered as independent informative priors for estimating shape and scale parameters of the Erlang distribution. In addition, various special cases are also discussed.
A Proposed Ridge Parameter To Improve The Least Square Estimator, Ghadban Khalaf
A Proposed Ridge Parameter To Improve The Least Square Estimator, Ghadban Khalaf
Journal of Modern Applied Statistical Methods
Ridge regression, a form of biased linear estimation, is a more appropriate technique than ordinary least squares (OLS) estimation in the case of highly intercorrelated explanatory variables in the linear regression model Y = β + u. Two proposed ridge regression parameters from the mean square error (MSE) perspective are evaluated. A simulation study was conducted to demonstrate the performance of the proposed estimators compared to the OLS, HK and HKB estimators. Results show that the suggested estimators outperform the OLS and the other estimators regarding the ridge parameters in all situations examined.
Obtaining Critical Values For Test Of Markov Regime Switching, Douglas G. Steigerwald, Valerie Bostwick
Obtaining Critical Values For Test Of Markov Regime Switching, Douglas G. Steigerwald, Valerie Bostwick
Douglas G. Steigerwald
For Markov regime-switching models, testing for the possible presence of more than one regime requires the use of a non-standard test statistic. Carter and Steigerwald (forthcoming, Journal of Econometric Methods) derive in detail the analytic steps needed to implement the test ofMarkov regime-switching proposed by Cho and White (2007, Econometrica). We summarize the implementation steps and address the computational issues that arise. A new command to compute regime-switching critical values, rscv, is introduced and presented in the context of empirical research.
Finding A Better Confidence Interval For A Single Regression Changepoint Using Different Bootstrap Confidence Interval Procedures, Bodhipaksha Thilakarathne
Finding A Better Confidence Interval For A Single Regression Changepoint Using Different Bootstrap Confidence Interval Procedures, Bodhipaksha Thilakarathne
Electronic Theses and Dissertations
Recently a number of papers have been published in the area of regression changepoints but there is not much literature concerning confidence intervals for regression changepoints. The purpose of this paper is to find a better bootstrap confidence interval for a single regression changepoint. ("Better" confidence interval means having a minimum length and coverage probability which is close to a chosen significance level). Several methods will be used to find bootstrap confidence intervals. Among those methods a better confidence interval will be presented.
Big Data And The Future, Sherri Rose
A Prior-Free Framework Of Coherent Inference And Its Derivation Of Simple Shrinkage Estimators, David R. Bickel
A Prior-Free Framework Of Coherent Inference And Its Derivation Of Simple Shrinkage Estimators, David R. Bickel
COBRA Preprint Series
The reasoning behind uses of confidence intervals and p-values in scientific practice may be made coherent by modeling the inferring statistician or scientist as an idealized intelligent agent. With other things equal, such an agent regards a hypothesis coinciding with a confidence interval of a higher confidence level as more certain than a hypothesis coinciding with a confidence interval of a lower confidence level. The agent uses different methods of confidence intervals conditional on what information is available. The coherence requirement means all levels of certainty of hypotheses about the parameter agree with the same distribution of certainty over parameter …
Targeted Maximum Likelihood Estimation For Dynamic Treatment Regimes In Sequential Randomized Controlled Trials, Paul Chaffee, Mark J. Van Der Laan
Targeted Maximum Likelihood Estimation For Dynamic Treatment Regimes In Sequential Randomized Controlled Trials, Paul Chaffee, Mark J. Van Der Laan
Paul H. Chaffee
Sequential Randomized Controlled Trials (SRCTs) are rapidly becoming essential tools in the search for optimized treatment regimes in ongoing treatment settings. Analyzing data for multiple time-point treatments with a view toward optimal treatment regimes is of interest in many types of afflictions: HIV infection, Attention Deficit Hyperactivity Disorder in children, leukemia, prostate cancer, renal failure, and many others. Methods for analyzing data from SRCTs exist but they are either inefficient or suffer from the drawbacks of estimating equation methodology. We describe an estimation procedure, targeted maximum likelihood estimation (TMLE), which has been fully developed and implemented in point treatment settings, …
Foundations Of Inference, Kevin H. Knuth, John Skilling
Foundations Of Inference, Kevin H. Knuth, John Skilling
Physics Faculty Scholarship
We present a simple and clear foundation for finite inference that unites and significantly extends the approaches of Kolmogorov and Cox. Our approach is based on quantifying lattices of logical statements in a way that satisfies general lattice symmetries. With other applications such as measure theory in mind, our derivations assume minimal symmetries, relying on neither negation nor continuity nor differentiability. Each relevant symmetry corresponds to an axiom of quantification, and these axioms are used to derive a unique set of quantifying rules that form the familiar probability calculus. We also derive a unique quantification of divergence, entropy and information.