Correlation-Type Goodness-of-Fit Test for Extreme Value Distribution Based on Simultaneous Closeness

• Activity Number: 43
• Type: Contributed
• Date/Time: Sunday, July 31, 2011 : 2:00 PM to 3:50 PM
• Sponsor: SSC
• Author(s): Katherine F. Davies*+ and Narayanaswamy Balakrishnan and Jerome P. Keating and Robert L. Mason
• Companies: University of Manitoba and McMaster University and The University of Texas at San Antonio and Southwest Research Institute
• Keywords: Correlation-type Test ; Weibull Distribution ; Extreme Value Distribution ; Simultaneous Closeness ; Plotting Points

Abstract

In reliability studies, one typically would assume a lifetime distribution for the units under study and then carry out the required analysis. One popular choice is the family of two-parameter Weibull distributions which, through a logarithmic transformation, can be transformed to the family of two-parameter extreme value distributions. In carrying out such a parametric analysis, it is desirable to test the validity of such a model assumption. A basic tool for this purpose is a quantile-quantile plot, but in its use, the issue of the choice of plotting position arises. By adopting the optimal plotting points based on Pitman closeness criterion proposed recently by Balakrishnan et al. (2010), we propose a correlation-type goodness-of-fit test for the extreme value distribution. We compute the proposed plotting points for various sample sizes and use them to determine the mean, standard deviation and critical values for the proposed correlation-type test statistic. We carry out a power study similar to Kinnison (1989), and then demonstrate the use of these plotting points and the associated correlation-type test for Weibull analysis with an illustrative example.