Goodness-Of-Fit Test For Standard Logistics Distribution With Outliers

Alternative to the least square coefficient of determination ( R2 OLS ), the coefficient of determination based on median absolute deviation,R 2 MAD , is an attractive consideration in the construction of goodness-of-fit test based on regression and correlation, due to its robustness. This study presents 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 R2 MAD for samples from the standard logistic distribution. The sampling distribution of R2 MAD is simulated for various sample sizes (n = 20, 40, 100), percentage of contamination (5%, 15%, 25%) and distribution of the contaminants (logistic (2, 0.2), logistic (0, 0.2), logistic (2, 1) and normal (3, 0.2) contaminants). The symmetricity of the sampling distribution of R2 MAD is observed and followed by the investigation of the confidence intervals of R2 MAD in the presence of outliers. The study of confidence interval estimates for the mean and standard deviation of R2 MAD was conducted using the bootstrap (BCa) method. Tables of critical values for samples from the standard logistic distribution using ZMAD = 1− R2 MAD and ZOLS = 1- R2OLS are constructed. The tables obtained then are used in the power study on the goodness-of-fit tests using test statistic for alternative distributions and contaminated alternative distributions. For lognormal, exponential and standard logistic alternatives, Z*MAD Z and Z *OLS are simulated for various sample sizes (n =10, 20, 30, 50, 100), percentage of contamination (5%, 15%, 25%, 40%) and distribution of the contaminants (logistic (2, 0.2), logistic (0, 0.2), logistic (2, 1) and normal (3, 0.2) contaminants) for different percentiles (a = 0.01, 0.025, 0.05, 0.1), respectively. The results indicated that the test statistic ZMAD is able to discriminate the sample that comes from alternative distributions as the test statistic ZOLS .

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