# Statistical Theory Commons™

1,616 Full-Text Articles 2,088 Authors 670,452 Downloads 54 Institutions

## All Articles in Statistical Theory

1,616 full-text articles. Page 1 of 42.

2020 Indiana University Bloomington

#### Estimating A Multilevel Model With Complex Survey Data: Demonstration Using Timss, Julie Lorah

##### Journal of Modern Applied Statistical Methods

Analysis of complex survey data is demonstrated for the multilevel model. Description of specific aspects of analysis, including plausible values, sampling weights, and replicate weights is provided. Following this, example TIMSS data and models are described and results are presented.

Concomitant Of Order Statistics From New Bivariate Gompertz Distribution, 2020 Babasaheb Bhimrao Ambedkar University

#### Concomitant Of Order Statistics From New Bivariate Gompertz Distribution, Sumit Kumar, M. J. S. Khan, Surinder Kumar

##### Journal of Modern Applied Statistical Methods

For the new bivariate Gompertz distribution, the expression for probability density function (pdf) of rth order statistics and pdf of concomitant arising from rth order statistics are derived. The properties of concomitant arising from the corresponding order statistics are used to derive these results. The exact expression for moment generating function (mgf) of concomitant of order rth statistics is derived. Also, the mean of concomitant arising from rth order statistics is computed using the mgf of concomitant of rth order statistics, and the exact expression for joint density of concomitant of two non-adjacent order statistics ...

Simple Unequal Allocation Procedure For Ranked Set Sampling With Skew Distributions, 2020 Rutgers University

#### Simple Unequal Allocation Procedure For Ranked Set Sampling With Skew Distributions, Dinesh Bhoj, Girish Chandra

##### Journal of Modern Applied Statistical Methods

A practical unbalanced Ranked Set Sampling (RSS) model is proposed to estimate the population mean of positively skewed distributions. The gains in the relative precisions of the population mean based on the proposed model for chosen distributions are uniformly higher than those based on balanced RSS and the t-model proposed in Kaur et al. (1997). The relative precisions of the simple unequal allocation model are, with one exception, better than (s, t)-model which is better than t-model. The relative precision of the proposed model is very close or equal to the optimal Neyman allocation model.

Almost All Missing Data Are Mnar, 2020 University of Rochester

#### Almost All Missing Data Are Mnar, Thomas R. Knapp

##### Journal of Modern Applied Statistical Methods

Rubin (1976, and elsewhere) claimed that there are three kinds of “missingness”: missing completely at random; missing at random; and missing not at random. He gave examples of each. The article that now follows takes an opposing view by arguing that almost all missing data are missing not at random.

A Primer On Statistical Inferences For Finite Populations, 2020 University of Rochester

#### A Primer On Statistical Inferences For Finite Populations, Thomas R. Knapp

##### Journal of Modern Applied Statistical Methods

This primer is intended to provide the basic information for sampling without replacement from finite populations.

Jmasm 54: A Comparison Of Four Different Estimation Approaches For Prognostic Survival Oral Cancer Model, 2020 Universiti Sains Malaysia

#### Jmasm 54: A Comparison Of Four Different Estimation Approaches For Prognostic Survival Oral Cancer Model, Wan Muhamad Amir, Muhammad Azeem, Masitah Hayati Harun, Zalila Ali, Mohamad Shafiq

##### Journal of Modern Applied Statistical Methods

Four types of estimation approaches for prognostic survival oral cancer model building are considered via a SAS algorithm: Efron’s Method, Exact Method, Breslow’s Method, and Discrete Method. Each method is illustrated separately and compared according to their coefficient parameter. An approach is considered by adding a bootstrapping technique for each handling ties method and a complete SAS algorithm is supplied for each proposed method, including methods for handling ties.

A New Two-Parametric ‘Useful’ Fuzzy Information Measure And Its Properties, 2020 University of Kashmir, Srinagar, India

#### A New Two-Parametric ‘Useful’ Fuzzy Information Measure And Its Properties, Saima Manzoor Sofi, Safina Peerzada, Mirza Abdul Khalique Baig

##### Journal of Modern Applied Statistical Methods

A ‘useful’ fuzzy measure of order α and type β is developed. Its validity established with a numerical example.

A New Two Parametric Weighted Generalized Entropy For Lifetime Distributions, 2020 University of Kashmir, Srinagar, India

#### A New Two Parametric Weighted Generalized Entropy For Lifetime Distributions, Bilal Ahmad Bhat, Mirza Abdul Khaliq Baig

##### Journal of Modern Applied Statistical Methods

The concept of weighted generalized entropy and its dynamic residual (version) is developed. The general expressions of these two uncertainty measures corresponding to some well-known lifetime distributions are derived. It is shown that the proposed dynamic entropy determines the survival function uniquely. Some significant properties and inequalities of this dynamic entropy are also discussed.

2020 University of North Florida

#### Uniform Random Variate Generation With The Linear Congruential Method, Joseph Free

##### PANDION: The Osprey Journal of Research and Ideas

This report considers the issue of using a speciﬁc linear congruential generator (LCG) to create random variates from the uniform(0,1) distribution. The LCG is used to generate multiple samples of pseudo-random numbers and statistical computation techniques are used to assess whether those samples could have resulted from a uniform(0,1) distribution. Source code is included with this report in the appendix along with annotations.

Objectives Driven Participatory Evaluation Model, 2020 Baker College

#### Objectives Driven Participatory Evaluation Model, Dustin R. Saalman

##### Journal of Modern Applied Statistical Methods

The ability to complete program evaluations of educational programming is typically restricted by the availability of resources, such as time, money and a trained evaluator. Although not a replacement for trained evaluators, promoting evaluative capacity and evaluative thinking within an organization can help mitigate this gap between talent and resources. Participatory evaluation is purported to increase organizational learning and promote evaluative thinking within an organization (Cousins & Whitmore, 1998). Objectives oriented evaluation is an easily understood evaluation method which provides a refined focus program outcome (Madaus & Stufflebeam, 1989). Using an internal evaluation of a new faculty onboarding course at a private ...

Even Order Ranked Set Sampling With Auxiliary Variable, 2020 National College of Business Administration & Economics, Lahore, Pakistan

##### Journal of Modern Applied Statistical Methods

Even order ranked set sampling (EORSS) is a novel proposed ranked set sampling scheme connected with an auxiliary variable correlated with the study variable. This scheme quantifies only the one sampling unit which is at even position from each ranking set by employing specific criteria. The performance of the ratio estimator under EORSS is compared to its contemporary estimators in simple random sampling (SRS), ranked set sampling (RSS), median ranked set sampling (MRSS) and quartile ranked set sampling (QRSS) exploiting the same number of quantified units. The simulation results proved that EORSS is an efficient alternative sampling scheme for ratio ...

Maximum Likelihood Estimations Based On Upper Record Values For Probability Density Function And Cumulative Distribution Function In Exponential Family And Investigating Some Of Their Properties, 2020 Cihan University-Erbil, Iraq

#### Maximum Likelihood Estimations Based On Upper Record Values For Probability Density Function And Cumulative Distribution Function In Exponential Family And Investigating Some Of Their Properties, Saman Hosseini, Parviz Nasiri, Sharad Damodar Gore

##### Journal of Modern Applied Statistical Methods

A useful subfamily of the exponential family is considered. The ML estimation based on upper record values are calculated for the parameter, Cumulative Density Function, and Probability Density Function of the subfamily. The relationship between MLE based on record values and a random sample are discussed, along with some properties of these estimators, and its utility is shown for large samples.

The Comparison Between Maximum Weighted And Trimmed Likelihood Estimator Of The Simple Circular Regression Model, 2020 University of Babylon, Iraq

#### The Comparison Between Maximum Weighted And Trimmed Likelihood Estimator Of The Simple Circular Regression Model, Ehab A. Mahmood, Habshah Midi, Abdul Ghapor Hussin

##### Journal of Modern Applied Statistical Methods

The Maximum Likelihood Estimator (MLE) was used to estimate unknown parameters of the simple circular regression model. However, it is very sensitive to outliers in data set. A robust method to estimate model parameters is proposed.

Bayesian Estimation Of The Parameters Of Discrete Weibull Type (I) Distribution, 2020 Cairo University, Cairo, Egypt

#### Bayesian Estimation Of The Parameters Of Discrete Weibull Type (I) Distribution, Samir Kamel Ashour, Mohamed Salem Abdelwahab Muiftah

##### Journal of Modern Applied Statistical Methods

Bayesian estimation of the continuous Weibull distribution parameters was studied by Ahmad and Ahmad (2013) under the assumption of knowing the shape parameter. Bayesian estimates are considered here of the parameters of the discrete Weibull Type I [DW(I)] distribution and are obtained under two different assumptions: when the shape parameter is known, and when both parameters are independent random variables. A Mathcad program is performed to simulate data from the DW(I) distribution considering different values of the parameters and different sample sizes, and to obtain Bayesian parameter estimates. The resulted estimates are compared to the ML and proportion ...

The Logic Model, Participatory Evaluation And Out Of School Art Programs, 2020 Wayne State University

#### The Logic Model, Participatory Evaluation And Out Of School Art Programs, Kimberly A. Kleinhans

##### Journal of Modern Applied Statistical Methods

The logic model and participatory evaluation are two popular methods of conducting program evaluation. Although both methods have their strengths, each has distinct weaknesses which can be ameliorated by combining them both together. The combined method is used to evaluate an out of school art program at a museum. Using both the logic model and participatory evaluation yielded beneficial results with more accurate representation of program outcomes.

Empirical Comparison Of Tests For One-Factor Anova Under Heterogeneity And Non-Normality: A Monte Carlo Study, 2020 University of South Florida

#### Empirical Comparison Of Tests For One-Factor Anova Under Heterogeneity And Non-Normality: A Monte Carlo Study, Diep Nguyen, Eunsook Kim, Yan Wang, Thanh Vinh Pham, Yi-Hsin Chen, Jeffrey D. Kromrey

##### Journal of Modern Applied Statistical Methods

Although the Analysis of Variance (ANOVA) F test is one of the most popular statistical tools to compare group means, it is sensitive to violations of the homogeneity of variance (HOV) assumption. This simulation study examines the performance of thirteen tests in one-factor ANOVA models in terms of their Type I error rate and statistical power under numerous (82,080) conditions. The results show that when HOV was satisfied, the ANOVA F or the Brown-Forsythe test outperformed the other methods in terms of both Type I error control and statistical power even under non-normality. When HOV was violated, the Structured ...

Jmasm 52: Extremely Efficient Permutation And Bootstrap Hypothesis Tests Using R, 2020 University of Crete, Greece

#### Jmasm 52: Extremely Efficient Permutation And Bootstrap Hypothesis Tests Using R, Christina Chatzipantsiou, Marios Dimitriadis, Manos Papadakis, Michail Tsagris

##### Journal of Modern Applied Statistical Methods

Re-sampling based statistical tests are known to be computationally heavy, but reliable when small sample sizes are available. Despite their nice theoretical properties not much effort has been put to make them efficient. Computationally efficient method for calculating permutation-based p-values for the Pearson correlation coefficient and two independent samples t-test are proposed. The method is general and can be applied to other similar two sample mean or two mean vectors cases.

A Generalized Family Of Lifetime Distributions And Survival Models, 2020 Western Carolina University

#### A Generalized Family Of Lifetime Distributions And Survival Models, Mahmoud Aldeni, Felix Famoye, Carl Lee

##### Journal of Modern Applied Statistical Methods

In lifetime data, the hazard function is a common technique for describing the characteristics of lifetime distribution. Monotone increasing or decreasing, and unimodal are relatively simple hazard function shapes, which can be modeled by many parametric lifetime distributions. However, fewer distributions are capable of modeling diverse and more complicated shapes such as N-shaped, reflected N-shaped, W-shaped, and M-shaped hazard rate functions. A generalized family of lifetime distributions, the uniform-R{generalized lambda} (U-R{GL}) are introduced and the corresponding survival models are derived, and applied to two lifetime data sets. The survival model is applied to a right censored lifetime data ...

Forward And Backward Continuation Ratio Models For Ordinal Response Variables, 2020 Eastern Connecticut State University

#### Forward And Backward Continuation Ratio Models For Ordinal Response Variables, Xing Liu, Haiyan Bai

##### Journal of Modern Applied Statistical Methods

There are different types of continuation ratio (CR) models for ordinal response variables. The different model equations, corresponding parameterizations, and nonequivalent results are confusing. The purpose of this study is to introduce different types of forward and backward CR models, demonstrate how to implement these models using Stata, and compare the results using data from the Educational Longitudinal Study of 2002 (ELS:2002).

2020 University of Southern California

#### Identifying Which Of J Independent Binomial Distributions Has The Largest Probability Of Success, Rand Wilcox

##### Journal of Modern Applied Statistical Methods

Let p1,…, pJ denote the probability of a success for J independent random variables having a binomial distribution and let p(1) ≤ … ≤ p(J) denote these probabilities written in ascending order. The goal is to make a decision about which group has the largest probability of a success, p(J). Let 1,…, J denote estimates of p1,…,pJ, respectively. The strategy is to test J − 1 hypotheses comparing the group with the largest estimate to each of the J − 1 remaining groups. For each of these J − 1 hypotheses that are rejected, decide that ... 