Measures of Income Inequality Based on Probability Weighted Moments

• Activity Number: 82
• Type: Contributed
• Date/Time: Sunday, August 3, 2014 : 4:00 PM to 5:50 PM
• Sponsor: Social Statistics Section
• Author(s): Tamer Abouelmagd*+ and Elsayed Ahi Habib Elamir and Ibrahim Ahmad
• Companies: Oklahoma State University and Benha University and Oklahoma State University
• Keywords: Income inequality measures ; incomplete moments ; probability weighted moments ; asymptotic normality ; confidence intervals ; simulation

Abstract

Methods to measure income inequality have for quite some time now been an important subject in statistics and econometric research. Various measures were proposed and studied. Among the more recent and practical ones we find Butler and McDonald (1989) and Ahmad (1994). These measures are based on incomplete moments or incomplete conditional moments and they take into consideration the shape of the income distribution but suffer sometimes from low efficiency and or lack or robustness. On the other hand, in recent years a new inferential method called "the probability weighted moments" (PWM) was introduced and studies as a competitor to more traditional inferential methods such as the method of moments or the maximum likelihood method, cf. Moisello (2007). In this investigation, a class of generalized measures of income inequalities based on the PWM are introduced and studied. These new measures are shown to include many previously discussed such as the Butler-McDonald-Ahmad measures as well as others. The statistical properties of these measures are studied both for finite samples via simulation and asymptotic behavior through mathematical proofs. Comparison with other measures de