# Research

## Frontiers in Statistics

### Friday, December 3, 2004

Title: Generalized Exponential Distribution: Sequential Estimation Based on Record-Breaking Data
Speaker: Alfred Mbah, (joint work with G. Yanev)
Time: 3:00pm‐4:00pm
Place: PHY 109

#### Abstract

Observing record-breaking values has a place in environmental studies, destructive stress testing, and industrial quality control experiments, among others. For an excellent recent monograph on statistical inference for record-breaking data we refer to Gulati and Padgett (2003). We present a sequential procedure for estimating the shape parameter of the generalized exponential distribution using records. The estimators are shown to be asymptotically risk efficient.

### Friday, November 19, 2004

Title: Introduction to Applied Longitudinal Data Analysis
Speaker: Ji-Hyun Lee, H. Lee Moffitt Cancer Center & Research Institute/
College of Medicine, USF
Time: 3:00pm‐4:00pm
Place: PHY 109

#### Abstract

Longitudinal studies are frequently conducted in epidemiology, social science, and biomedical research areas and the data sets are comprised of repeated observations of an outcome and a set of covariates. One objective of statistical analysis is to describe how the response variable of interest is affected by other covariates over time. A challenge in the analysis of longitudinal data is that the data are correlated, as multiple observations are measured from each individual, and this correlation has to be taken into account in the analysis to yield valid inference. In recent years, there have been remarkable developments in methods for analyzing data from longitudinal studies. This seminar will be devoted to introducing the major types of models used in the analysis of correlated responses and historical review. The topics will be approached from the practitioner's points-of-view: the main emphasis will be on the practical rather than the theoretical aspects. Come and join in this educational event with opportunities for lively discussions with a Biostatistician at the Moffitt Cancer Center!

### Friday, October 29, 2004

Title: An Analysis of the Effects of Grading with the Plus/Minus system verses the Standard Four Point system
Speaker: Rebecca Wooten
Time: 3:00pm‐4:00pm
Place: PHY 109

### Friday, October 15, 2004

Title: Software Reliability Modeling Using Regression Method
Speaker: A. M. Mostafa, (joint work with A. N. V. Rao and K. Ramachandran)
Time: 3:00pm‐4:00pm
Place: PHY 109

#### Abstract

We will start with some motivation remarks for the use of mathematical models in the analysis and prediction of software reliability evolution during testing phase. We will review some basic reliability concepts and the most important models used in software reliability. Finally, we will be discussing the regression method and make a comparison with the results given in Suresh and Henry's dissertations.

### Friday, September 17, 2004

Title: Reliability Model Using Truncated Skew-Laplace Distribution
Speaker: Gokarna Aryal, (joint work with A. N. V. Rao)
Time: 3:00pm‐4:00pm
Place: PHY 109

#### Abstract

A random variable $$X$$ is said to have the skew-Laplace distribution if its pdf is $$f(x)=2g(x)G(\lambda x)$$, where $$g(.)$$ and $$G(.)$$, respectively, denote the pdf and cdf of the Laplace distribution. In this paper we provide a comprehensive analysis of the mathematical properties of a truncated skew-Laplace distribution when it is truncated on the left at $$0$$. A reliability model using this distribution is compared with a two parameter Gamma model.

### Friday, September 3, 2004

Title: Random mappings of a finite set into itself: some distributional results and applications
Speaker: Lyuben Mutafchiev, Bulgarian Academy of Sciences/
American University in Bulgaria
Time: 3:00pm‐4:00pm
Place: PHY 109

#### Abstract

This talk deals with mappings of a set of cardinality $$n$$ into itself. Introducing appropriate probability measures on the set of all such mappings, we consider several random mapping models. We study the asymptotic behavior, as $$n$$ goes to infinity, of certain statistics associated with these models, focusing on limiting distributions. Two applications to analysis of algorithms including random number generators and integer factorization will also be discussed.