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University of Wyoming

Statistics Events


Lyman McDonald

Start: Friday, November 13, 2009 - 2:00 PM
End: Friday, November 13, 2009 - 3:00 PM
Location: Ross Hall, Room 339
Contact: Lori Dockter, DockterL@uwyo.edu, 307-766-4229

Event Details:

Some weighted distribution theory: Illustrated with applications in environmental statistics.

Dr. Lyman L. McDonald, Senior Biometrician, Western EcoSystems Technology, Inc., 200 South Second Street, Suite B, Laramie, Wyoming, USA 82070. http://www.west-inc.com
I briefly review weighted distribution theory and numerous common applications in biased sampling situations. Applications include most study designs where it is not possible to guarantee that study units from a population are selected with equal probability; including, classical unequal probability sample survey methods, size-biased sampling, line transect sampling, and renewal theory. G. P. Patil and C. R. Rao in 1977 (In Applications of Statistics, edited by P. R. Krishnaiah, North-Holland Publishing Company)  wrote "Although the situations that involve weighted distributions seem to occur frequently in various fields, the underlying concept of weighted distributions as a major stochastic concept does not seem to have been widely recognized." The same quote is applicable today. The last two statisticians hired by WEST, Inc. never heard the words "weighted distribution" in their university training and were poorly trained in unequal probability sample survey methods. I present applications in study of wildlife and fish populations that should motivate undergraduate and graduate students of mathematical statistics who have an interest in environmental issues. These applications include line transect and distance sampling in surveys of wildlife populations where probability of detection is less than 100% (whales, polar bear, etc.), estimation of the fitness function in study of natural selection, and fitting of habitat and food selection models in study of wildlife and fish populations.