Robust correlation coefficient goodness-of-fit test for the Gumbel distribution

Abstract

Background & Aim: A single outlier can even have a large disturbing effect on a classical statistical method that is optimal under the classical assumptions. One of the powerful goodness-offit tests is the correlation coefficient test, however this test suffers from the presence of outliers. Methods & Materials: This study provides a simple robust method for test of goodness of fit for the Gumbel distribution [extreme value distribution (EVD) type I family] through using the new diagnostic tool called the “Forward Search” (FS) method. The FS version of this test was introduce in the present study, which is not affected by the outliers. Results: A new robust method for testing the goodness-of-fit for Gumbel distribution has been presented. The approach gives information about the distribution of majority of the data and the percentage of contamination. Conclusion: A new robust method for testing the goodness-of-fit for the Gumbel distribution has been presented. The simple and fast method have been used to find distribution of proposed statistic. In addition, using the transformation study, an application to the two-parameter Weibull distribution has been investigated. The performance and the ability of this procedure to capture the structure of data have been illustrated by some simulation studies.

Keywords

• Outlier
• Regression analysis
• Statistical distributions