THE ELEMENTARY AND FUNCTIONAL ADDITIVE INDEX FACTOR ANALYSIS AND ITS UNIQUE SOLUTIONS WITH DISCRETE ODD FUNCTION OF THE MATHEMATICAL SIGNUM
Emil Hristov
Abstract: The two discrete statistical factor analyses - additive and index of each dependent variable from two multiplicatively connected factor variables are combined in a common elementary functional analysis with discrete data. That is the first and most necessary factor analysis in the statistical practice and in all applications and scientific studies with discrete data.
The initial and definitive form of the functional analysis is the additive one because its solutions contain explicitly only real existing precise net effects and eventual joint effects (increases and decreases) of the dependent variable of unidirectional and multidirectional changes in the factors р(prices) and (amounts). The additive factor analysis is decided after turning the multiplicative model into linear additive factor model using a theoretical mathematical criterion - discrete odd function mathematical signum (h). Index factor analysis can be carried out independently without prior additive factor analysis.
Any multiplicative models in all applied statistics in which discrete dependent variable are represented by the product of two discrete factor variable could be solved with the displayed methodology. The next article will display and summarize both forms (additive and index) of elementary functional analysis of the production of homogeneous set (finite set) of one and the same commodity and a diverse set (finite set) of various commodities.
The initial and definitive form of the functional analysis is the additive one because its solutions contain explicitly only real existing precise net effects and eventual joint effects (increases and decreases) of the dependent variable of unidirectional and multidirectional changes in the factors р(prices) and (amounts). The additive factor analysis is decided after turning the multiplicative model into linear additive factor model using a theoretical mathematical criterion - discrete odd function mathematical signum (h). Index factor analysis can be carried out independently without prior additive factor analysis.
Any multiplicative models in all applied statistics in which discrete dependent variable are represented by the product of two discrete factor variable could be solved with the displayed methodology. The next article will display and summarize both forms (additive and index) of elementary functional analysis of the production of homogeneous set (finite set) of one and the same commodity and a diverse set (finite set) of various commodities.
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Date published: 2015-04-22
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