Water Resources Research Act Program

Details for Project ID 2003DC40B

Analysis of Positive, Right Skewed, and Unimodal Observations

Institute: District of Columbia
Year Established: 2003 Start Date: 2003-03-01 End Date: 2004-02-28
Total Federal Funds: $7,303 Total Non-Federal Funds: $14,616

Principal Investigators: Reza Modarres

Project Summary: This research will use non-parametric or semi-parametric estimator of the mean of a positive, right skewed and unimodal distribution to develop statistical methodology of environmental data. Due to skewness, the sample mean underestimates the population mean. Such consistent underestimation of the mean has far-reaching environmental repercussion as underestimation of means tantamount to underestimation of risk. Conservative estimates of the upper quantiles are often used in regulatory settings to reflect a degree of prudence in the decision making process. This is especially true when the issues involved concern human health or protection of natural resources. We are interested in estimating the quantiles of right-skewed distribution of data by seeking symmetrizing transformation. Parameters of interest are estimated on the transformed scale and estimates of quantile are obtained on the original scale after a re-transformation. This project will better allow us to understand the relationship between symmetry and right skewness of the underlying distribution as well as train a graduate student in conducting research in statistical methodology.