An atom approach to assessing the outlier properties of probability models

Graduation date: 1984This thesis is concerned with the problem of developing a\ud method to categorize probability models by their outlier properties.\ud There have been two such categorization methods proposed in the\ud literature. Neyman and Scott (1971) classify an entire family of\ud distributions into the outlier properties outlier-prone completely\ud (OPC) and outlier resistant. Green (1974) classifies particular\ud distributions into relative outlier resistance and proneness (ROR\ud and ROP) and absolute outlier resistance and proneness (AOR and\ud AOP). Green has pointed out that the Neyman and Scott approach\ud allows no finite member families to be OPC. We have found that\ud Green's approach does not allow discrete distributions to be AOR.\ud We have extended Green's results to show outlier relationships\ud for functions of random variables, functions of densities and\ud functions of distribution functions. We have more clearly defined\ud Green's six possible classes of distributions by their outlier\ud properties. We have looked at the outlier properties of mixtures of\ud distributions. We have presented a categorized listing of the\ud common probability distributions by classes and provide an extension\ud of Green's outlier characteristic property for mutivariate distributions\ud whose densities are a function of the quadratic form\ud X'1-'x.\ud In response to the problem that no discrete distribution can be\ud AOR, we have developed an atom approach to assessing the outlier\ud properties of distributions. We have defined low, medium and high\ud tendency for outlier distributions and have provided classification\ud schemes for determining the outlier tendencies for a particular distribution\ud of interest. A listing of common distributions that have\ud low, medium and high tendency for outliers has also been provided