Characterizations Based on Regression Assumptions of Order Statistics

• Activity Number: 184
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Wen-Jang Huang*+ and Nan-Cheng Su
• Companies: National University of Kaohsiung and National Taipei University
• Keywords: Exponential distribution ; gamma distribution ; inverse gamma distribution ; normal distribution ; student t-distribution ; uniform distribution

Abstract

Characterizations of the Student's t distribution based on some simple properties of certain regression functions associated with the order statistics of a sequence of n independent and identically distributed random variables with a common absolutely continuous distribution function, have been investigated by many authors. In this work, first we give some conditional expectation properties of order statistics, which can be used to establish some equivalent forms for conditional expectations for sum of random variables based on order statistics. Using these equivalent forms, some known results can be extended immediately. Next a new characterization of distributions based on regression assumptions of order statistics is presented