TY  - INPR
A1  - Läuter, Henning
A1  - Ramadan, Ayad
T1  - Statistical Scaling of Categorical Data
N2  - Estimation and testing of distributions in metric spaces are well known. R.A. Fisher, J. Neyman, W. Cochran and M. Bartlett achieved essential results on the statistical analysis of categorical data. In the last 40 years many other statisticians found important results in this field. 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. With this method we identify probabilities connected with the categorical data and probabilities in metric spaces. Here we get a mapping from the levels of factors or names into points of a metric space. This mapping yields the scale for the categorical data. From the statistical point of view we use multivariate statistical methods, we calculate maximum likelihood estimations and compare different approaches for scaling.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2010, 01 
Y1  - 2010
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49566
ER  - 
TY  - THES
A1  - Ramadan, Ayad
T1  - Statistical model for categorical data
Y1  - 2010
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Ramadan, Ayad M.
T1  - Range of lower bounds
JF  - Applied mathematics and computation
N2  - Each of n jobs is to be processed without interruption on a single machine. Each job becomes available for processing at time zero. The objective is to find a processing order of the jobs which minimizes the sum of weighted completion times added with maximum weighted tardiness. In this paper we give a general case of the theorem that given in [6]. This theorem shows a relation between the number of efficient solutions, lower bound LB and optimal solution. It restricts the range of the lower bound, which is the main factor to find the optimal solution. Also, the theorem opens algebraic operations and concepts to find new lower bounds.
KW  - Lower bound
KW  - Multi objective function
KW  - Efficient solutions
Y1  - 2011
U6  - https://doi.org/10.1016/j.amc.2011.03.066
SN  - 0096-3003
VL  - 218
IS  - 3
SP  - 1008
EP  - 1011
PB  - Elsevier
CY  - New York
ER  - 
TY  - INPR
A1  - Läuter, Henning
A1  - Ramadan, Ayad
T1  - Modeling and Scaling of Categorical Data
N2  - Estimation and testing of distributions in metric spaces are well known. R.A. Fisher, J. Neyman, W. Cochran and M. Bartlett achieved essential results on the statistical analysis of categorical data. In the last 40 years many other statisticians found important results in this field. 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. With this method we identify probabilities connected with the categorical data and probabilities in metric spaces. Here we get a mapping from the levels of factors or names into points of a metric space. This mapping yields the scale for the categorical data. From the statistical point of view we use multivariate statistical methods, we calculate maximum likelihood estimations and compare different approaches for scaling.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2010, 03 
Y1  - 2010
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49572
ER  -