Statistics and Probability Commons^™

Generalized Transmuted Family Of Distributions: Properties And Applications, Morad Alizadeh, Faton Merovci, Gholamhossein G. Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

We introduce and study general mathematical properties of a new generator of continuous distributions with two extra parameters called the Generalized Transmuted Family of Distributions. We investigate the shapes and present some special models. The new density function can be expressed as a linear combination of exponentiated densities in terms of the same baseline distribution. We obtain explicit expressions for the ordinary and incomplete moments and generating function, Bonferroni and Lorenz curves, asymptotic distribution of the extreme values, Shannon and R´enyi entropies and order statistics, which hold for any baseline model. Further, we introduce a bivariate extension of the new …

Changing Of The Guards: Strip Cover With Duty Cycling∗, Amotz Bar-Noy, Benjamin Baumer, Dror Rawitz

Mathematics Sciences: Faculty Publications

The notion of duty cycling is common in problems which seek to maximize the lifetime of a wireless sensor network. In the duty cycling model, sensors are grouped into shifts that take turns covering the region in question, and each sensor can belong to at most one shift. We consider the imposition of the duty cycling model upon the Strip Cover problem, where we are given n sensors on a one-dimensional region, and each shift can contain at most k ≤ n sensors. We call the problem of finding the optimal set of shifts so as to maximize the length …

Thermally Induced Aggregation Of Rigid Spheres On A Liquid Surface, Eric Forgoston, Leo Hentschker, Siobhan Soltau, Patrick Truitt, Ashuwin Vaidya

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Fluids provide the optimal setting to explore natural patterns far from thermodynamic equilibrium. Experiments suggest that randomly dispersed particles on a liquid surface tend to aggregate on the surface of liquid over time, and the process is enhanced by an increase in the temperature of the liquid. We show that the agglomeration radii increases monotonically with temperature up until the point where all particles in the system form a single, large aggregate. The aggregation dynamics is related to changes in the material properties of the liquid including its viscosity and surface tension as well as the convection driven flow generated …

Open Access!: Review Of Online Statistics: An Interactive Multimedia Course Of Study By David Lane, Samuel L. Tunstall

Numeracy

David M. Lane (project leader). Online Statistics Education: An Interactive Multimedia Course of Study (http://onlinestatbook.com/)
Also: David M. Lane (primary author and editor), with David Scott, Mikki Hebl, Rudy Guerra, Dan Osherson, and Heidi Zimmer. Introduction to Statistics. Online edition (http://onlinestatbook.com/Online_Statistics_Education.pdf), 694 pp.

It is rare that students receive high-quality textbooks for free, but David Lane's Online Statistics: An Interactive Multimedia Course of Study permits precisely that. This review gives an overview of the many features in Lane's online textbook, including the Java Applets, the textbook itself, and the resources available for instructors. A discussion …

Infographics As Eye Candy: Review Of World War Ii In Numbers: An Infographic Guide To The Conflict, Its Conduct, And Its Casualties By Peter Doyle (2013), Joel Best

Numeracy

Peter Doyle. World War II in Numbers: An Infographic Guide to the Conflict, Its Conduct, and Its Casualties, illustrated by Lindsey Johns (Buffalo NY: Firefly Books, 2013). 224 pp. ISBN: 177085195X.

Doyle’s book contains dozens of graphs of statistical data dealing with World War II. Many of these graphs are visually striking. However, they often violate fundamental graphing principles, in that they distort quantitative relationships, use unidentified scales, and often make it difficult to compare quantities. Graphic software makes it easy to create imaginative images, but these can fail to communicate the very information that is the graph’s purpose.

Modelling Subject-Specific Childhood Growth Using Linear Mixed-Effect Models With Cubic Regression Splines, Laura M. Grajeda, Andrada Ivanescu, Mayuko Saito, Ciprian Crainiceanu, Devan Jaganath, Robert H. Gilman, Jean E. Crabtree, Dermott Kelleher, Lilia Cabrera, Vitaliano Cama, William Checkley

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Background: Childhood growth is a cornerstone of pediatric research. Statistical models need to consider individual trajectories to adequately describe growth outcomes. Specifically, well-defined longitudinal models are essential to characterize both population and subject-specific growth. Linear mixed-effect models with cubic regression splines can account for the nonlinearity of growth curves and provide reasonable estimators of population and subject-specific growth, velocity and acceleration. Methods: We provide a stepwise approach that builds from simple to complex models, and account for the intrinsic complexity of the data. We start with standard cubic splines regression models and build up to a model that includes subject-specific …

Analysis Of The Precipitation Detection Algorithm For The Geonor T-200b Precipitation Gauge To Improve Accuracy, Megan Lerman, Robert K. Goodrich

STAR Program Research Presentations

In an effort to improve the precipitation detection algorithm for the Geonor All Weather Precipitation Gauge, an automated truth algorithm has been created to detect errors in the original algorithm. The original algorithm detects precipitation in real time and uses the rate of precipitation to indicate an event. The automated truth does not detect in real time, and focuses on precipitation accumulation to indicate an event. Since the automated truth is delayed, it is able to consider the data collected before and after the point it is analyzing. The automated truth is already more accurate than the original algorithm but …

Spatiotemporal Meta-Analysis: Reviewing Health Psychology Phenomena Over Space And Time., Blair T. Johnson

CHIP Documents

This supplemental material is meant to support this article:

Johnson, B. T., Crowley, E., & Marrouch, N. Spatiotemporal meta-analysis: Reviewing health psychology phenomena over space and time. Health Psychology Review.

Specifically, it is a database of GDPs per capita for nations in the world between 1800 and 2015. It is archived here to support an online supplement to this article.

GDP per capita

Asymptotic Behavior Of Certain Integrodifferential Equations, Said R. Grace, Elvan Akin

Mathematics and Statistics Faculty Research & Creative Works

This paper deals with asymptotic behavior of nonoscillatory solutions of certain forced integrodifferential equations of the form: (a(t)x'(t))' = e (t) + ∫ ^t_c (t - s)^{α - 1}k(t,s)ƒ(s,x(s))ds, c > 1, 0 < α < 1. From the obtained results, we derive a technique which can be applied to some related integrodifferential as well as integral equations.

Nonoscillation Criteria For Two-Dimensional Time-Scale Systems, Ozkan Ozturk, Elvan Akin

Mathematics and Statistics Faculty Research & Creative Works

We study the existence and nonexistence of nonoscillatory solutions of a two-dimensional system of first-order dynamic equations on time scales. Our approach is based on the Knaster and Schauder fixed point theorems and some certain integral conditions. Examples are given to illustrate some of our main results.

Qualitative Analysis On Differential, Fractional Differential, And Dynamic Equations And Related Topics, Said R. Grace, Taher S. Hassan, Shurong Sun, Elvan Akin

Mathematics and Statistics Faculty Research & Creative Works

This issue on qualitative analysis on differential, fractional differential, and dynamic equations and related topics aims at an all-around research and the state-of-the-art theoretical, numerical, and practical achievements that contribute to this field.

Sneak-Out Principle On Time Scales, Martin Bohner, Samir H. Saker

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we show that the so-called "sneak-out principle" for discrete inequalities is valid also on a general time scale. In particular, we prove some new dynamic inequalities on time scales which as special cases contain discrete inequalities obtained by Bennett and Grosse-Erdmann. The main results also are used to formulate the corresponding continuous integral inequalities, and these are essentially new. The techniques employed in this paper are elementary and rely mainly on the time scales integration by parts rule, the time scales chain rule, the time scales Hölder inequality, and the time scales Minkowski inequality.

Oscillation Criteria For Fourth Order Nonlinear Positive Delay Differential Equations With A Middle Term, Said R. Grace, Elvan Akin

Mathematics and Statistics Faculty Research & Creative Works

In this article, we establish some new criteria for the oscillation of fourth order nonlinear delay differential equations of the form (Equation presented) provided that the second order equation (Equation presented) is nonoscillatiory or oscillatory. This equation with g(t) = t is considered in [8] and some oscillation criteria for this equation via certain energy functions are established. Here, we continue the study on the oscillatory behavior of this equation via some inequalities.

An Efficient Basket Trial Design, Kristen Cunanan, Alexia Iasonos, Ronglai Shen, Colin B. Begg, Mithat Gonen

Memorial Sloan-Kettering Cancer Center, Dept. of Epidemiology & Biostatistics Working Paper Series

The landscape for early phase cancer clinical trials is changing dramatically due to the advent of targeted therapy. Increasingly, new drugs are designed to work against a target such as the presence of a specific tumor mutation. Since typically only a small proportion of cancer patients will possess the mutational target, but the mutation is present in many different cancers, a new class of basket trials is emerging, whereby the drug is tested simultaneously in different baskets, i.e., sub-groups of different tumor types. Investigators not only desire to test whether the drug works, but also to determine which types of …

Variable Selection For Case-Cohort Studies With Failure Time Outcome, Andy Ni, Jianwen Cai, Donglin Zeng

Memorial Sloan-Kettering Cancer Center, Dept. of Epidemiology & Biostatistics Working Paper Series

Case-cohort designs are widely used in large cohort studies to reduce the cost associated with covariate measurement. In many such studies the number of covariates is very large, so an efficient variable selection method is necessary. In this paper, we study the properties of variable selection using the smoothly clipped absolute deviation penalty in a case-cohort design with a diverging number of parameters. We establish the consistency and asymptotic normality of the maximum penalized pseudo-partial likelihood estimator, and show that the proposed variable selection procedure is consistent and has an asymptotic oracle property. Simulation studies compare the finite sample performance …

Leveraging Contact Network Structure In The Design Of Cluster Randomized Trials, Guy Harling, Rui Wang, Jukka-Pekka Onnela, Victor Degruttola

Harvard University Biostatistics Working Paper Series

Background: In settings like the Ebola epidemic, where proof-of-principle trials have succeeded but questions remain about the effectiveness of different possible modes of implementation, it may be useful to develop trials that not only generate information about intervention effects but also themselves provide public health benefit. Cluster randomized trials are of particular value for infectious disease prevention research by virtue of their ability to capture both direct and indirect effects of intervention; the latter of which depends heavily on the nature of contact networks within and across clusters. By leveraging information about these networks – in particular the degree …

Using Validation Data To Adjust The Inverse Probability Weighting Estimator For Misclassified Treatment, Danielle Braun, Corwin Zigler, Francesca Dominici, Malka Gorfine

Harvard University Biostatistics Working Paper Series

The inverse probability weighting (IPW) estimator is widely used to estimate the treatment effect in observational studies in which patient characteristics might not be balanced by treatment group. The estimator assumes that treatment assignment, is error-free, but in reality treatment assignment can be measured with error. This arises in the context of comparative effectiveness research, using administrative data sources in which accurate procedural or billing codes are not always available. We show the bias introduced to the estimator when using error-prone treatment assignment, and propose an adjusted estimator using a validation study to eliminate this bias. In simulations, we explore …

Estimation And Inference For The Mediation Proportion, Daniel Nevo, Xiaomei Liao, Donna Spiegelman

Harvard University Biostatistics Working Paper Series

In epidemiology, public health and social science, mediation analysis is often undertaken to investigate the extent to which the effect of a risk factor on an outcome of interest is mediated by other covariates. A pivotal quantity of interest in such an analysis is the mediation proportion. A common method for estimating it, termed the "difference method'', compares estimates from models with and without the hypothesized mediator. However, rigorous methodology for estimation and statistical inference for this quantity has not previously been available. We formulated the problem for the Cox model and generalized linear models, and utilize a data duplication …

A Cautionary Note On The Effect Of Treatment Misclassification On The Average Treatment Effect, Danielle Braun, Corwin Zigler, Malka Gorfine, Francesca Dominici

Harvard University Biostatistics Working Paper Series

Comparative effectiveness research often relies on large administrative data, such as claims data. Methods to estimate treatment effects assume that treatment assignment is error-free, but in reality the inaccuracy of procedural or billing codes frequently misclassifies patients into treatment groups. Propensity score methods are widely used to analyze observational studies in which patient characteristics might not be balanced by treatment group. We evaluate the impact of treatment misclassification on 1) propensity score estimation; 2) treatment effect estimation conditional on propensity score estimation and implementation. We focus on three common propensity score implementations: subclassification, matching, and inverse probability of treatment weighting …

The Myth Of Making Inferences For An Overall Treatment Efficacy With Data From Multiple Comparative Studies Via Meta-Analysis, Takahiro Hasegawa, Brian Claggett, Lu Tian, Scott D. Solomon, Marc A. Pfeffer, Lee-Jen Wei

Harvard University Biostatistics Working Paper Series

Meta analysis techniques, if applied appropriately, can provide a summary of the totality of evidence regarding an overall difference between a new treatment and a control group using data from multiple comparative clinical studies. The standard meta analysis procedures, however, may not give a meaningful between-group difference summary measure or identify a meaningful patient population of interest, especially when the fixed effect model assumption is not met. Moreover, a single between-group comparison measure without a reference value obtained from patients in the control arm would likely not be informative enough for clinical decision making. In this paper, we propose a …