Mary Ann Flanigan Wagner

Bio: Mary Ann Flanigan Wagner is an academic researcher from Purdue University. The author has contributed to research in topics: Probability distribution & Univariate. The author has an hindex of 6, co-authored 9 publications receiving 192 citations.

Using Univariate Bézier Distributions to Model Simulation Input Processes

Abstract: We describe a graphical, interactive technique for modeling univariate simulation input processes by using a family of probability distributions based on Bezier curves. This family has an open-ende...

Using univariate Be´zier distributions to model simulation input processes

Abstract: We describe a graphical, interactive technique for modeling bivariate simulation input processes using a distribution family based on Bezier curves and surfaces. This family has an open-ended parameterization and is capable of accurately representing an unlimited variety of shapes for marginal distributions together with many common types of bivariate stochastic dependence. Our input-modeling technique is implemented in a Windows-based software system called PRIME-PRobabilistic Input Modeling Environment. Several examples illustrate the application of PRIME to subjective and data-driven estimation of bivariate distributions representing simulation inputs.

Graphical interactive simulation input modeling with bivariate Bézier distributions

Abstract: A graphical interactive technique for modeling bivariate simulation inputs is based on a family of continuous univariate and bivariate probability distributions with bounded support that are described by Be´zier curves and surfaces, respectively. This family of distributions has a natural, extensible parameterization so that all parameters have a meaningful interpretation; and the complete family is capable of accurately representing an unlimited variety of shapes for marginal distributions together with many common types of bivariate stochastic dependence. This approach to simulation input modeling is implemented in a Windows-based software system called PRIME-PRobabilistic Input Modeling Environment. Several examples illustrate the application of PRIME to subjective and data-driven estimation of bivariate distributions representing simulation inputs.

Recent developments in input modeling with Bézier distributions

Abstract: New methods are presented for estimating univariate and bivariate Bezier distributions. A likelihood ratio test is used to estimate the number of control points for a univariate Bezier distribution fitted to sample data. To estimate the control points of a bivariate Bezier distribution with fixed marginals based on either sample data or subjective information about the joint dependency structure, a linear-programming approach is formulated. These methods are implemented in the Windows-based software system called PRIME-PRobabilistic Input Modeling Environment. Several examples illustrate the application of these estimation procedures.

Structure of southern bean mosaic virus at 2.8 A resolution.

Abstract: X-ray diffraction studies reveal that the polypeptide chain of the southern bean mosaic virus protein subunit has a fold closely similar to the shell domain of tomato bushy stunt virus. The protruding domain of tomato bushy stunt virus is absent in southern bean mosaic virus. The tertiary structure observed in these viruses may be particularly suitable f or the formation of the protein coat in small, spherical, RNA-containing, plant viruses.

Random Number Generation

Abstract: The fields of probability and statistics are built over the abstract concepts of probability space and random variable. This has given rise to elegant and powerful mathematical theory, but exact implementation of these concepts on conventional computers seems impossible. In practice, random variables and other random objects are simulated by deterministic algorithms. The purpose of these algorithms is to produce sequences of numbers or objects whose behavior is very hard to distinguish from that of their “truly random” counterparts, at least for the application of interest. Key requirements may differ depending on the context.For Monte Carlo methods, the main goal is to reproduce the statistical properties on which these methods are based, so that the Monte Carlo estimators behave as expected, whereas for gambling machines and cryptology, observing the sequence of output values for some time should provide no practical advantage for predicting the forthcoming numbers better than by just guessing at random.

Multivariate non-normally distributed random variables in climate research - introduction to the copula approach

Abstract: . Probability distributions of multivariate random variables are generally more complex compared to their univariate counterparts which is due to a possible nonlinear dependence between the random variables. One approach to this problem is the use of copulas, which have become popular over recent years, especially in fields like econometrics, finance, risk management, or insurance. Since this newly emerging field includes various practices, a controversial discussion, and vast field of literature, it is difficult to get an overview. The aim of this paper is therefore to provide an brief overview of copulas for application in meteorology and climate research. We examine the advantages and disadvantages compared to alternative approaches like e.g. mixture models, summarize the current problem of goodness-of-fit (GOF) tests for copulas, and discuss the connection with multivariate extremes. An application to station data shows the simplicity and the capabilities as well as the limitations of this approach. Observations of daily precipitation and temperature are fitted to a bivariate model and demonstrate, that copulas are valuable complement to the commonly used methods.

Univariate Distribution Relationships

Abstract: Probability distributions are traditionally treated separately in introductory mathematical statistics textbooks. A figure is presented here that shows properties that individual distributions possess and many of the relationships between these distributions.