Statistics and Probability Commons^™

Inventing Around Edison’S Lamp Patent: The Role Of Patents In Stimulating Downstream Development And Competition, Ron D. Katznelson, John Howells

Ron D. Katznelson

We provide the first detailed empirical study of inventing around patent claims. The enforcement of Edison’s incandescent lamp patent in 1891-1894 stimulated a surge of patenting. Most of these later patents disclosed inventions around the Edison patent. Some of these patents introduced important new technology in their own right and became prior art for new fields, indicating that invention around patents contributes to dynamic efficiency. Contrary to widespread contemporary understanding, the Edison lamp patent did not suppress technological advance in electric lighting. The market position of General Electric (“GE”), the Edison patent-owner, weakened through the period of this patent’s enforcement.

Simulating Burr Type Vii Distributions Through The Method Of L-Moments And L-Correlations, Mohan D. Pant, Todd C. Headrick

Mohan Dev Pant

Burr Type VII, a one-parameter non-normal distribution, is among the less studied distributions, especially, in the contexts of statistical modeling and simulation studies. The main purpose of this study is to introduce a methodology for simulating univariate and multivariate Burr Type VII distributions through the method of L-moments and L-correlations. The methodology can be applied in statistical modeling of events in a variety of applied mathematical contexts and Monte Carlo simulation studies. Numerical examples are provided to demonstrate that L-moment-based Burr Type VII distributions are superior to their conventional moment-based analogs in terms of distribution fitting and estimation. Simulation results …

Compound Interest And The Power Of Saving, Richard H. Serlin

Richard H. Serlin

This is an article with an included assignment that I give to my personal finance 1 students. The first part talks about the power of compound interest. I go into depth about the intuition why it's so powerful, why it takes off, and has been called the eighth wonder of the world. I've haven't seen anywhere else an extensive explanation of the intuition like I have here.

In the second part I give the students a nice assignment to see how much their savings can grow if they invest even a modest amount consistently, month in and month out, in …

An L-Moment Based Characterization Of The Family Of Dagum Distributions, Mohan D. Pant, Todd C. Headrick

Mohan Dev Pant

This paper introduces a method for simulating univariate and multivariate Dagum distributions through the method of L-moments and L-correlation. A method is developed for characterizing non-normal Dagum distributions with controlled degrees of L-skew, L-kurtosis, and L-correlations. The procedure can be applied in a variety of contexts such as statistical modeling (e.g., income distribution, personal wealth distributions, etc.) and Monte Carlo or simulation studies. Numerical examples are provided to demonstrate that -moment-based Dagum distributions are superior to their conventional moment-based analogs in terms of estimation and distribution fitting. Evaluation of the proposed method also demonstrates that the estimates of L-skew, L-kurtosis, …

A Method For Simulating Burr Type Iii And Type Xii Distributions Through L-Moments And L-Correlations, Mohan D. Pant, Todd C. Headrick

Mohan Dev Pant

This paper derives the Burr Type III and Type XII family of distributions in the contexts of univariate L-moments and the L-correlations. Included is the development of a procedure for specifying nonnormal distributions with controlled degrees of L-skew, L-kurtosis, and L-correlations. The procedure can be applied in a variety of settings such as statistical modeling (e.g., forestry, fracture roughness, life testing, operational risk, etc.) and Monte Carlo or simulation studies. Numerical examples are provided to demonstrate that L-moment-based Burr distributions are superior to their conventional moment-based analogs in terms of estimation and distribution fitting. Evaluation of the proposed procedure also …

A Doubling Technique For The Power Method Transformations, Mohan D. Pant, Todd C. Headrick

Mohan Dev Pant

Power method polynomials are used for simulating non-normal distributions with specified product moments or L-moments. The power method is capable of producing distributions with extreme values of skew (L-skew) and kurtosis (L-kurtosis). However, these distributions can be extremely peaked and thus not representative of real-world data. To obviate this problem, two families of distributions are introduced based on a doubling technique with symmetric standard normal and logistic power method distributions. The primary focus of the methodology is in the context of L-moment theory. As such, L-moment based systems of equations are derived for simulating univariate and multivariate non-normal distributions with …

An L-Moment-Based Analog For The Schmeiser-Deutsch Class Of Distributions, Todd C. Headrick, Mohan D. Pant

Mohan Dev Pant

This paper characterizes the conventional moment-based Schmeiser-Deutsch (S-D) class of distributions through the method of L-moments. The system can be used in a variety of settings such as simulation or modeling various processes. A procedure is also described for simulating S-D distributions with specified L-moments and L-correlations. The Monte Carlo results presented in this study indicate that the estimates of L-skew, L-kurtosis, and L-correlation associated with the S-D class of distributions are substantially superior to their corresponding conventional product-moment estimators in terms of relative bias—most notably when sample sizes are small.

A Method For Simulating Nonnormal Distributions With Specified L-Skew, L-Kurtosis, And L-Correlation, Todd C. Headrick, Mohan D. Pant

Mohan Dev Pant

This paper introduces two families of distributions referred to as the symmetric κ and asymmetric κL-κR distributions. The families are based on transformations of standard logistic pseudo-random deviates. The primary focus of the theoretical development is in the contexts of L-moments and the L-correlation. Also included is the development of a method for specifying distributions with controlled degrees of L-skew, L-kurtosis, and L-correlation. The method can be applied in a variety of settings such as Monte Carlo studies, simulation, or modeling events. It is also demonstrated that estimates of L-skew, L-kurtosis, and L-correlation are superior to conventional product-moment estimates of …

Simulating Non-Normal Distributions With Specified L-Moments And L-Correlations, Todd C. Headrick, Mohan D. Pant

Mohan Dev Pant

This paper derives a procedure for simulating continuous non-normal distributions with specified L-moments and L-correlations in the context of power method polynomials of order three. It is demonstrated that the proposed procedure has computational advantages over the traditional product-moment procedure in terms of solving for intermediate correlations. Simulation results also demonstrate that the proposed L-moment-based procedure is an attractive alternative to the traditional procedure when distributions with more severe departures from normality are considered. Specifically, estimates of L-skew and L-kurtosis are superior to the conventional estimates of skew and kurtosis in terms of both relative bias and relative standard error. …

On The Order Statistics Of Standard Normal-Based Power Method Distributions, Todd C. Headrick, Mohan D. Pant

Mohan Dev Pant

This paper derives a procedure for determining the expectations of order statistics associated with the standard normal distribution (Z) and its powers of order three and five (Z^3 and Z^5). The procedure is demonstrated for sample sizes of n ≤ 9. It is shown that Z^3 and Z^5 have expectations of order statistics that are functions of the expectations for Z and can be expressed in terms of explicit elementary functions for sample sizes of n ≤ 5. For sample sizes of n = 6, 7 the expectations of the order statistics for Z, Z^3, and Z^5 only require a …

A Doubling Method For The Generalized Lambda Distribution, Todd C. Headrick, Mohan D. Pant

Mohan Dev Pant

This paper introduces a new family of generalized lambda distributions (GLDs) based on a method of doubling symmetric GLDs. The focus of the development is in the context of L-moments and L-correlation theory. As such, included is the development of a procedure for specifying double GLDs with controlled degrees of L-skew, L-kurtosis, and L-correlations. The procedure can be applied in a variety of settings such as modeling events and Monte Carlo or simulation studies. Further, it is demonstrated that estimates of L-skew, L-kurtosis, and L-correlation are substantially superior to conventional product-moment estimates of skew, kurtosis, and Pearson correlation in terms …

Characterizing Tukey H And Hh-Distributions Through L-Moments And The L-Correlation, Todd C. Headrick, Mohan D. Pant

Mohan Dev Pant

This paper introduces the Tukey family of symmetric h and asymmetric hh-distributions in the contexts of univariate L-moments and the L-correlation. Included is the development of a procedure for specifying nonnormal distributions with controlled degrees of L-skew, L-kurtosis, and L-correlations. The procedure can be applied in a variety of settings such as modeling events (e.g., risk analysis, extreme events) and Monte Carlo or simulation studies. Further, it is demonstrated that estimates of L-skew, L-kurtosis, and L-correlation are substantially superior to conventional product-moment estimates of skew, kurtosis, and Pearson correlation in terms of both relative bias and efficiency when heavy-tailed distributions …

Influence Of Non-Linearity To The Optimal Experimental Design Demonstrated By A Biological System, René Schenkendorf, Andreas Kremling, Michael Mangold

René Schenkendorf

A precise estimation of parameters is essential to generate mathematical models with a highly predictive power. A framework that attempts to reduce parameter uncertainties caused by measurement errors is known as Optimal Experimental Design (OED). The Fisher Information Matrix (FIM), which is commonly used to define a cost function for OED, provides at the best only a lower bound of parameter uncertainties for models that are non-linear in their parameters. In this work, the Sigma Point method is used instead, because it enables a more reliable approximation of the parameter statistics accompanied by a manageable computational effort. Moreover, it is …

The Overhaul Of U.S. Patent Law, Ron D. Katznelson

Ron D. Katznelson

No abstract provided.

Statistics In Law: Bad Inferences & Uncommon Sense, Curtis E.A. Karnow

Curtis E.A. Karnow

A review of classic fallacies in statistics and probability in the courts. The article briefly, and in plain English, provides an introduction to probability theory, and randomness.

Conference Proceedings 3rd International Scientific Conference On “Energy Systems With It” At Alvsjö Fair In Association With Energitinget March 16-17 2010, Dr. Erik Dahlquist, Dr. Jenny Palm

Dr. Erik Dahlquist

2010 “The Energiting” is performed for the 12th time. The International Scientific conference is arranged for the 3rd time. The organisers are Swedish Energy Agency, Mälardalen University and the Research School for Energy Systems with LiU, KTH, UU and CTH. The first topic will be “Energy systems” covering use of renewable energy sources, energy conversion and process efficiency improvement with new technologies, as well as societal aspects of the introduction of new technologies. The second topic is “Energy and IT”. This covers energy and load management, interaction between production, distribution and “consumption”, usage of data for decision support and control, …

Comments Submitted To The Us Patent Office On Enhancing The Quality Of Examination, Ron D. Katznelson

Ron D. Katznelson

No abstract provided.

On Simulating Univariate And Multivariate Burr Type Iii And Type Xii Distributions, Todd C. Headrick, Mohan D. Pant, Yanyan Sheng

Mohan Dev Pant

This paper describes a method for simulating univariate and multivariate Burr Type III and Type XII distributions with specified correlation matrices. The methodology is based on the derivation of the parametric forms of a pdf and cdf for this family of distributions. The paper shows how shape parameters can be computed for specified values of skew and kurtosis. It is also demonstrated how to compute percentage points and other measures of central tendency such as the mode, median, and trimmed mean. Examples are provided to demonstrate how this Burr family can be used in the context of distribution fitting using …

Patent Examination Policy And The Social Costs Of Examiner Allowance And Rejection Errors, Ron D. Katznelson

Ron D. Katznelson

No abstract provided.

Proceedings Of The Scientific Conference On Energy And It At Alvsjo Fair, Stockholm March 11-12, 2009 In Connection With The “Energitinget 2009, Dr. Erik Dahlquist, Dr. Jenny Palm

Dr. Erik Dahlquist

This book contains the proceedings from the Energy and IT conference at Alvsjo Energy conference "Energitinget" arranged by Swedish Energy Agency, with approximately 2500 visitors. The papers contain both technical and social science papers, relating to both energy efficiency in buildings and in industry.

Proceedings From Scientific Conference On Green Energy And It, Dr. Erik Dahlquist

Dr. Erik Dahlquist

This conference is part of the annual Energitinget, a national arena for energy in Sweden, with some 2500 participants. The focus with this session is to give a forum for researchers to present scientific results, and also to discuss these with other researchers. It contains papers in the area of Energy and IT as well as Green energy generally

Microproteomics: Analysis Of Protein Diversity In Small Samples, Howard B. Gutstein, Jeffrey S. Morris, Suresh P. Annangudi, Jonathan V. Sweedler

Jeffrey S. Morris

Proteomics, the large-scale study of protein expression in organisms, offers the potential to evaluate global changes in protein expression and their post-translational modifications that take place in response to normal or pathological stimuli. One challenge has been the requirement for substantial amounts of tissue in order to perform comprehensive proteomic characterization. In heterogeneous tissues, such as brain, this has limited the application of proteomic methodologies. Efforts to adapt standard methods of tissue sampling, protein extraction, arraying, and identification are reviewed, with an emphasis on those appropriate to smaller samples ranging in size from several microliters down to single cells. The …

Comment On Global Dynamics Of Biological Systems, Radhakrishnan Nagarajan

Radhakrishnan Nagarajan

No abstract provided.

Use Of Modeling And Simulation In Pulp And, Dr. Erik Dahlquist

Dr. Erik Dahlquist

The book is a handbook for operators and process engineers in primarily pulp and paper industry, but also other process industries about how to utilise simulation as a tool for enhanced process operations. The book has been written as part of a EU COST action on Process Simulation, with 14 countries and 50 researchers and process industry representatives involved.

Statistical Issues In Proteomic Research, Jeffrey S. Morris

Jeffrey S. Morris

No abstract provided.

Laser Capture Sampling And Analytical Issues In Proteomics, Howard Gutstein, Jeffrey S. Morris

Jeffrey S. Morris

Proteomics holds the promise of evaluating global changes in protein expression and post-translational modificaiton in response to environmental stimuli. However, difficulties in achieving cellular anatomic resolution and extracting specific types of proteins from cells have limited the efficacy of these techniques. Laser capture microdissection has provided a solution to the problem of anatomical resolution in tissues. New extraction methodologies have expanded the range of proteins identified in subsequent analyses. This review will examine the application of laser capture microdissection to proteomic tissue sampling, and subsequent extraction of these samples for differential expression analysis. Statistical and other quantitative issues important for …

Prepms: Tof Ms Data Graphical Preprocessing Tool, Yuliya V. Karpievitch, Elizabeth G. Hill, Adam J. Smolka, Jeffrey S. Morris, Kevin R. Coombes, Keith A. Baggerly, Jonas S. Almeida

Jeffrey S. Morris

We introduce a simple-to-use graphical tool that enables researchers to easily prepare time-of-flight mass spectrometry data for analysis. For ease of use, the graphical executable provides default parameter settings experimentally determined to work well in most situations. These values can be changed by the user if desired. PrepMS is a stand-alone application made freely available (open source), and is under the General Public License (GPL). Its graphical user interface, default parameter settings, and display plots allow PrepMS to be used effectively for data preprocessing, peak detection, and visual data quality assessment.

Wavelet-Based Functional Mixed Model Analysis: Computational Considerations, Richard C. Herrick, Jeffrey S. Morris

Jeffrey S. Morris

Wavelet-based Functional Mixed Models is a new Bayesian method extending mixed models to irregular functional data (Morris and Carroll, JRSS-B, 2006). These data sets are typically very large and can quickly run into memory and time constraints unless these issues are carefully dealt with in the software. We reduce runtime by 1.) identifying and optimizing hotspots, 2.) using wavelet compression to do less computation with minimal impact on results, and 3.) dividing the code into multiple executables to be run in parallel using a grid computing resource. We discuss rules of thumb for estimating memory requirements and computation times in …

Wavelet-Based Functional Mixed Models, Jeffrey S. Morris, Raymond J. Carroll

Jeffrey S. Morris

Increasingly, Increasingly, scientific studies yield functional data, in which the ideal units of observation are curves and the observed data consist of sets of curves that are sampled on a fine grid. We present new methodology that generalizes the linear mixed model to the functional mixed model framework, with model fitting done by using a Bayesian wavelet-based approach. This method is flexible, allowing functions of arbitrary formand the full range of fixed effects structures and between-curve covariance structures that are available in the mixed model framework. It yields nonparametric estimates of the fixed and random-effects functions as well as the …

Analysis Of Mass Spectrometry Data Using Bayesian Wavelet-Based Functional Mixed Models, Jeffrey S. Morris, Philip J. Brown, Keith A. Baggerly, Kevin R. Coombes

Jeffrey S. Morris

In this chapter, we demonstrate how to analyze MALDI-TOF/SELDITOF mass spectrometry data using the wavelet-based functional mixed model introduced by Morris and Carroll (2006), which generalizes the linear mixed models to the case of functional data. This approach models each spectrum as a function, and is very general, accommodating a broad class of experimental designs and allowing one to model nonparametric functional effects for various factors, which can be conditions of interest (e.g. cancer/normal) or experimental factors (blocking factors). Inference on these functional effects allows us to identify protein peaks related to various outcomes of interest, including dichotomous outcomes, categorical …