Statistics and Probability Commons^™

Certain Characterizations Of Recently Introduced Distributions, Gholamhossein G. Hamedani, Seyed Morteza Najibi

Mathematics, Statistics and Computer Science Faculty Research and Publications

Various characterizations of twenty two recently introduced distributions are presented. These characterizations are based on: (I) ration of two truncated moments; (ii) the hazard function and (iii) conditional expectations.

A New Weibull-G Family Of Distributions, M. H. Tahir, Muhammad Zubair, M. Mansoor, Gauss M. Cordeiro, Morad Alizadeh, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Statistical analysis of lifetime data is an important topic in reliability engineering, biomedical and social sciences and others. We introduce a new generator based on the Weibull random variable called the new Weibull-G family. We study some of its mathematical properties. Its density function can be symmetrical, left-skewed, right-skewed, bathtub and reversed-J shaped, and has increasing, decreasing, bathtub, upside-down bathtub, J, reversed-J and S shaped hazard rates. Some special models are presented. We obtain explicit expressions for the ordinary and incomplete moments, quantile and generating functions, Renyi entropy, order statistics and reliability. Three useful characterizations based on truncated moments are …

Worldwide Cutaneous Malignant Melanoma Incidences Analyzed By Sex, Age, And Skin Type Over Time (1955–2007): Is Hpv Infection Of Androgenic Hair Follicular Melanocytes A Risk Factor For Developing Melanoma Exclusively In People Of European-Ancestry?, Stephen Merrill, Madhan Subramanian, Dianne E. Godar

Mathematics, Statistics and Computer Science Faculty Research and Publications

The cutaneous malignant melanoma (CMM) incidence has been increasing in an exponential manner in certain populations around the world for over 7 decades. To help illuminate the etiology, we performed worldwide temporal (1955–2007) CMM incidence analysis by sex, age (0–14, 15–29, 30–49, 50–69, 70–85+), and skin type on 6 continents using data from the International Agency for Research on Cancer. We observe an exponential increase in the CMM incidence over time and an increase of about 2 orders of magnitude between age groups 0–14 and 15–29 exclusively in European-ancestry populations around the world independent of skin type (I–III or III–IV). …

Cohomology Operations On Random Spaces, Matthew John Zabka

Wayne State University Dissertations

Topology has recently received more attention from statisticians as some its tools have been applied to understanding the shape of data. In particular, a data set can generate a topological space, and this space’s topological structure can give us insight into some properties of the data. This framework has made it necessary to study random spaces generated by data. For example, without an understanding of the probabilistic properties of random spaces, one cannot conclude with any degree of confidence what the tools of topology tell us about a data set. While some results are known about the cohomological structure of …

Salvage Brachytherapy For Biochemically Recurrent Prostate Cancer Following Primary Brachytherapy, John M. Lacy, William A. Wilson, Raevti Bole, Li Chen, Ali S. Meigooni, Randall G. Rowland, William H. St. Clair

Urology Faculty Publications

Purpose. In this study, we evaluated our experience with salvage brachytherapy after discovery of biochemical recurrence after a prior brachytherapy procedure. Methods and Materials. From 2001 through 2012 twenty-one patients treated by brachytherapy within University of Kentucky or from outside centers developed biochemical failure and had no evidence of metastases. Computed tomography (CT) scans were evaluated; patients who had an underseeded portion of their prostate were considered for reimplantation. Results. The majority of the patients in this study (61.9%) were low risk and median presalvage PSA was 3.49 (range 17.41–1.68). Mean follow-up was 61 months. At last follow-up after reseeding, …

Causal Inference In Observational Studies With Clustered Data, Meng Wu

Legacy Theses & Dissertations (2009 - 2024)

In this thesis, we study causal inference in observational studies with clustered data.

Estimating Survival Distributions, Important Covariates And Time-Varying Associations, Yan Wu

Legacy Theses & Dissertations (2009 - 2024)

There are three papers each on a different topic in this thesis. The first paper proposes a new objective methodology to estimate any subject specific survival distribution with potential time-varying effect by adjusting approximated polynomial censored survival function with estimated censoring distribution under three different assumptions: uniform censoring, independent censoring and non-informative censoring. The coefficients of the polynomial censored survival function and underlying censoring probability are estimated at each event or censoring time point across the study time frame, which naturally accommodates potential non-proportional hazards along with time-varying effect. An extensive simulation study indicates that the proposed methods usually perform …

Collective Action And Decision Making: An Analysis Of Economic Modeling And Environmental Free-Riding, Thomas Miller 16

Honor Scholar Theses

No abstract provided.

The Smallest Non-Autograph, Benjamin Baumer, Yijin Wei, Gary S. Bloom

Mathematics Sciences: Faculty Publications

Suppose that G is a simple, vertex-labeled graph and that S is a multiset. Then if there exists a one-to-one mapping between the elements of S and the vertices of G, such that edges in G exist if and only if the absolute difference of the corresponding vertex labels exist in S, then G is an autograph, and S is a signature for G. While it is known that many common families of graphs are autographs, and that infinitely many graphs are not autographs, a non-autograph has never been exhibited. In this paper, we identify the smallest non-autograph: a graph …

On Variable Bandwidth Kernel Density And Regression Estimation, Janet Nakarmi

Electronic Theses and Dissertations

We study the ideal variable bandwidth kernel density estimator introduced by McKay (1993) and the plug-in practical version of the variable bandwidth kernel density estimator with two sequences of bandwidths as in Ginè and Sang (2013).We estimate the variance of the variable bandwidth kernel density estimator. Based on the exact formula of the bias and the variance of the variable bandwidth kernel density estimator, we develop the optimal bandwidth selection of the true variable bandwidth kernel density estimator. Furthermore, we present the central limit theorem of the true variable bandwidth kernel density estimator. We also propose a new variable bandwidth …

The Reflected-Shifted-Truncated-Gamma Distribution For Negatively Skewed Survival Data With Application To Pediatric Nephrotic Syndrome, Sophia D. Waymyers

Theses and Dissertations

Negatively skewed survival data arise occasionally in public health fields and in statistical research. Standard distributions such as the exponential, generalized F, generalized gamma, Gompertz, log-logistic, lognormal, Rayleigh, and Weibull distributions are not always well suited to this data. The primary goal of this dissertation is to find a viable alternative for modeling negatively skewed survival data such as the time to first remission for pediatric patients with frequently relapsing or steroid dependent nephrotic syndrome.

We begin with a brief introduction of survival analysis and the nature of pediatric nephrotic syndrome. A meta-analysis on atopy and pediatric nephrotic syndrome using …

Registration And Clustering Of Functional Observations, Zizhen Wu

Theses and Dissertations

As an important exploratory analysis, curves of similar shape are often classified into groups, which we call clustering of functional data. Phase variations or time distortions are often encountered in the biological processes, such as growth patterns or gene profiles. As a result of time distortion, curves of similar shape may not be aligned. Regular clustering methods for functional data usually ignore the presence of phase variations, which may result in low clustering accuracy. However, it is difficult to account for phase variation without knowing the cluster structure.

In this dissertation, we first propose a Bayesian method that simultaneously clusters …

Some Issues In Markov Chain Monte Carlo Estimation For Item Response Theory, Han Kil Lee

Theses and Dissertations

Both the marginalized Bayesian modal estimation (MBME) and Metropolis-Hasting within Gibbs (MH/Gibbs) are the popular estimation methods for Item Response Theory (IRT). However, predictions from MBME and MH/Gibbs are not directly comparable because of two problems. First, the examinees with the same response pattern do not produce the same ability estimates from MH/Gibbs while MBME provides identical estimates. This problem can be handled by updating each response pattern instead of updating each examinee. Second, standard errors from MBME are smaller than standard error estimates from MH/Gibbs. This pattern occurs because of two speculated reasons; correlation between item parameter estimations and …

Score Test Derivations And Implementations For Bivariate Probability Mass And Density Functions With An Application To Copula Functions, Roy Bower

Theses and Dissertations

This dissertation is comprised and grounded in statistical theory with an application to solving real world problems. In particular, the development and implementation of multiple score tests under a variety of scenarios are derived, applied, and interpreted. In chapter 2, I propose a score test for independence of the marginals based on Lakshminarayana’s bivariate Poisson distribution. Each marginal distribution of the bivariate model is a univariate Poisson distribution, and the parameters of the bivariate distribution can be estimated using maximum likelihood methods. The simulation study shows that the score test maintains size close to the nominal level. To assess the …

Bayesian Ensemble Of Regression Trees For Multinomial Probit And Quantile Regression, Bereket P. Kindo

Theses and Dissertations

This dissertation proposes multinomial probit Bayesian additive regression trees (MPBART), ordered multiclass Bayesian additive classification trees (O-MBACT) and Bayesian quantile additive regression trees (BayesQArt) as extensions of BART - Bayesian additive regression trees for tackling multinomial choice, multiclass classification, ordinal regression and quantile regression problems. The proposed models exhibit very good predictive performances. In particular, ranking among the top performing procedures when non-linear relationships exist between the response and the predictors. The proposed procedures can readily be applied on data sets with the number of predictors larger than the number of observations.

MPBART is sufficiently flexible to allow inclusion of …

Modeling Daily Electricity Load Curve Using Cubic Splines And Functional Principal Components, Abdelmonaem Salem Jornaz

Doctoral Dissertations

"Forecasting electricity load is very important to the electric utilities as well as producers of power because accurate predictions can cut down costs by avoiding power shortages or surpluses. Of specific interest is the 24-hour daily electricity load profile, which provides insight into periods of high demand and periods where the use of electricity is at a minimum. Researchers have proposed many approaches to modeling electricity prices, real-time load, and day-ahead demand, with varying success. In this dissertation three new approaches to modeling and forecasting the 24-hour daily electricity load profiles are presented. The application of the proposed methods is …

Garch(1,1) With Sifted Gamma-Distributed Errors, Alan C. Budd

College of Graduate Studies: Theses & Dissertations

Typical General Autoregressive Conditional Heteroskedastic (GARCH) processes involve normally-distributed errors, and they model strictly-positive error processes poorly. This thesis will present a method for estimating the parameters of a GARCH(1,1) process with shifted Gamma-distributed errors, conduct a simulation study to test the method, and apply the method to real time series data.

Semi-Parametrics Dose Finding Methods, Matthieu Clertant, John O'Quigley

COBRA Preprint Series

We describe a new class of dose finding methods to be used in early phase clinical trials. Under some added parametric conditions the class reduces to the family of continual reassessment method (CRM) designs. Under some relaxation of the underlying structure the method is equivalent to the CCD, mTPI or BOIN classes of designs. These latter designs are non-parametric in nature whereas the CRM class can be viewed as being strongly parametric. The proposed class is characterized as being semi-parametric since it corresponds to CRM with a nuisance parameter. Performance is good, matching that of the CRM class and improving …

Consensus Regularized Selection Based Prediction, Ping Wang

Wayne State University Theses

Integrating regularization methods within a regression framework has become a popular choice for researchers to build predictive models with lower variance and better generalization. Regularizers also aid in building interpretable models with high-dimensional data which makes them very appealing. Regularizers in general are unique in nature as they cater to data specific features such as correlation, structured sparsity, and temporal smoothness. The problem of obtaining a consensus among such diverse regularizers is extremely important in order to determine the optimal regularizer for the model. This is called the consensus regularization problem which has not received much attention in the literature, …

Development In Normal Mixture And Mixture Of Experts Modeling, Meng Qi

Theses and Dissertations--Statistics

In this dissertation, first we consider the problem of testing homogeneity and order in a contaminated normal model, when the data is correlated under some known covariance structure. To address this problem, we developed a moment based homogeneity and order test, and design weights for test statistics to increase power for homogeneity test. We applied our test to microarray about Down’s syndrome. This dissertation also studies a singular Bayesian information criterion (sBIC) for a bivariate hierarchical mixture model with varying weights, and develops a new data dependent information criterion (sFLIC).We apply our model and criteria to birth- weight and gestational …