Physical Sciences and Mathematics Commons^™

New Tests Of Univariate Symmetry Based On The Gini Mean Difference, Hend Ouda

Dissertations

Gini mean difference (GMD) was proposed as a measure of income inequality by Corrado Gini in 1912. Since then it has been widely applied - mostly in theeconomics, but also in statistical and social science research.

Four statistical tests of univariate symmetry are being proposed---all based on the comparison of variation below and above the median (known or estimated) measured by the GMD. These tests are applicable to the data from populations with median known and unknown, and each of them has its rank-basedcounterpart, so they can also be used for ordinal data.

A Monte Carlo simulation study was performed …

New Estimators Of A Circular Median, Sauwanit Ratanaruamkarn

Dissertations

The specific properties of probability distributions on a circle require different definitions of several statistical concepts. For example, a median that can always be found for linear data not always exists on the circle. Several estimators of a circular median were proposed, lately by Otieno (2002), Otieno and Anderson - Cook (2003). Their work is, however, focused on the "preferred direction" which coincides with the median, mean and mode in the case of symmetric, unimodal distributions. This dissertation is focused on the estimators of a population median in a wider range of population distributions on a circle including distributions with …