Seminar Series: Fall 2010
The seminar series will usually take place on Fridays in a Business Building room, but the exact time and location could be different due to a variety of factors including room availability in the Business Building. For actual direction to the Business Building, please see campus map. For additional information contact Dr. Kefeng Xu, (210) 458-5388.
Friday, Sept. 24, 2010, 2:00-3:00pm, Business Building 2.01.14
Presenter: Dr. David Han Assistant Professor, Department of Management Science & Statistics College of Business University of Texas at San Antonio
Presentation Title: EXACT INFERENCE FOR FAILURE DATA FROM EXPONENTIAL DISTRIBUTION UNDER PROGRESSIVE TYPE-I CENSORING
Abstract: For reasons of time constraint and cost reduction, censoring is commonly employed in practice, especially in reliability engineering. Among various censoring schemes, progressive Type-I right censoring provides not only the practical advantage of known termination time but also greater flexibility to the experimenter in the design stage by allowing for the removal of test units at non-terminal time points. In this talk, we consider a progressively Type-I censored life-test under the assumption that the lifetime of each test unit is exponentially distributed. For small to moderate sample sizes, a practical modification is proposed to the censoring scheme in order to guarantee a feasible life-test under progressive Type-I censoring. Under this setup, we obtain the maximum likelihood estimator (MLE) of the unknown mean parameter and derive the exact sampling distribution of the MLE under the condition that its existence is ensured. Using the exact distribution of the MLE as well as its asymptotic distribution and the parametric bootstrap method, the construction of confidence intervals for the mean parameter is then discussed and their performance is assessed through Monte Carlo simulations.
Friday, Oct. 15, 2010, Business Building (Time and Room: TBA)
Friday, Nov. 5, 2010, 3:00-4:00pm, Business Building 3.01.02
Presenter: Katherine Davies, Assistant Professor, Department of Statistics, University of Manitoba Winnipeg, Manitoba, Canada
Presentation Title: Order Statistics and Pitman Closeness
- Abstract: In this talk, I will discuss some recent work of mine on order statistics and Pitman's measure of closeness. The first part of my talk will introduce the concept of Pitman's measure of closeness wherein I will provide some background and important definitions. Followed by this, I will discuss our first work wherein we compared sample order statistics, in the Pitman sense, to population quantiles of a location-scale family of distributions. Explicit expressions will be shown for some specific families such as uniform, exponential and power function. The next part of my talk will discuss an extension of this work which we called simultaneous closeness. In this work, we derived expressions for the probability that an individual order statistic is closest to the target parameter among the order statistics from a complete random sample. I will present results for random variables with bounded and complete support. Focusing on location-scale parameter families and fixing the parameter of interest as quantiles, I will present results for families such as normal and exponential. The last part of my talk involves our more recent work where we explored an application of the concept of simultaneous closeness. In particular, we looked at the use of simultaneous closeness probabilities as plotting points for the purposes of goodness-of-fit. From this, I will describe a distribution-based approach which selects plotting points (quantiles) based on the simultaneous closeness of order statistics to population quantiles. I will finish by presenting the usefulness of this test by examining the power properties of a correlation goodness-of-fit test for normality.
Keating, J.P., Mason, R.L. and P.K. Sen (1993) Pitman's measure of closeness, Society for Industrial and Applied Mathematics, Philadelphia.
Balakrishnan, N., Davies, Katherine and Jerome Keating (2009) Pitman Closeness of Order statistics to Population quantiles, Communications in Statistics: Simulation and Computation, 38:802-820.
- Balakrishnan, N., Davies, K.F., Keating, J.P. and R. L. Mason (2010) Simultaneous Closeness among Order Statistics to Population Quantiles, Journal of Statistical Planning and Inference, Vol.140, 9:2408-2415.
Friday, December ?? (to be announced), 2010, 1:30-2:30pm, Business Building xx.xx.xx