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Often data sets contain categorical data, e.g., levels of factors or names. There does not exist any ordering or any distance between these categories. At each level there are measured some metric or categorical values. We introduce a new method of scaling based on statistical decisions. For this we define empirical probabilities for the original observations and find a class of distributions in a metric space where these empirical probabilities can be found as approximations for equivalently defined probabilities.

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Ayad M. Ramadan was born in Kirkuk-Iraq 1972, obtained his Bsc. in Mathematics at the University of Mosul 1995, and the Msc. in Operations research at Al-Mustansiriyah University-Baghdad 1998. The PhD. at Potsdam University-Germany 2010. Research interesting: Operations Research, Optimization Theory, Statistics.

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