Goodness-of-fit Test for Standard Logistic Distribution with Outliers: Correlation Coefficient Based on Median Absolute Deviation

Alternative to the least square coefficient of determination, R-squared OLS, the coefficient of determination based on median absolute deviation, R-squared MAD, is an attractive consideration in the construction of goodness-of-fit test based on regression and correlation, due to its robustness. This book focused on the observations made from the resulting plots and descriptive measures obtained from contaminated standard logistic distribution. Contamination is introduced to investigate perseverance of robustness property of R-squared MAD for samples from the standard logistic distribution. The early section of the book is devoted to the investigation of the symmetricity of the sampling distribution of R-squared MAD and its confidence intervals in the presence of outliers. This is followed by constructing tables of critical values for samples from the standard logistic distribution. Then a power study on the goodness-of-fit test using test statistic ZMAD and ZOLS is conducted via simulation. The results indicated that the test statistic ZMAD is able to discriminate the sample that comes from alternative distributions as the test statistic ZOLS.