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 Title: Statistical mechanics of choice and market segmentation by choice profiles Author(s): Faynzilberg, Peter Samuel Doctoral Committee Chair(s): Monahan, George E. Department / Program: Business Administration Discipline: Business Administration Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Business Administration, Marketing Mathematics Statistics Abstract: There are several main contributions of the work presented in this thesis. Specifically, we have: (1) Solved the problem of prediction of heterogeneity of consumer population in terms of choice behavior when the market shares held by the brands comprising the market are known. (2) Addressed a long-standing dispute in the marketing literature on the validity of entropy-based models of buyer behavior. (3) Introduced a behavioral mode segmentation by choice profiles. (4) Obtained a closed form of two families of distributions, namely simplex-geometric and simplex-exponential distributions, that have applicability far beyond the context in which we arrived at them.The substantive problem addressed by this thesis is that of determining population heterogeneity on terms of choice behavior. Each member of the consumer population is assumed to behave probabilisticly. Her propensity to buy one of, say, n alternative brands comprising the market is described by a tuple of probabilities q = ($q\sb1,q\sb2$, ...,$q\sb{n}$) that we call choice profile. Heterogeneity of the population in terms of choice profiles is then described by a function g(q) that, for any choice profile in a n-dimensional simplex $S\sp{n}$, gives the respective proportion of the population. In this thesis we derive function g(q) in the case when the market shares $\int\sb{S\sp{n}}$ qg(q)dq are known.The derivation of population heterogeneity is based on the formalism of entropy maximization the applicability of which to modelling social situations has been seriously questioned. We contribute to the resolution of this dispute by explicating the development of information functions and entropy from first principles. In addition, we analyze and further detail maximum-entropy formalism. We classify certain knowledge used in this methodology into three types of constraints on entropy maximization. We also make an inference from Jaynes'es analysis that entropy maximization is a meta-theoretic criterion of model building. Being free from semantics of the model, it is equally applicable to the study of physical systems and human populations.The segmentation scheme we suggest here is based on restricting probabilities to take on values from a lattice of cites on the simplex. The cites need not be equidistant, and this segmentation may be used independently of entropic modelling.Finally, we introduce two families of distributions supported by simplexes in Euclidean space. Although previously encountered in a variety of contexts, the closed form of these distributions is given in this thesis, perhaps, for the first time. Issue Date: 1992 Type: Text Language: English URI: http://hdl.handle.net/2142/22507 Rights Information: Copyright 1992 Faynzilberg, Peter Samuel Date Available in IDEALS: 2011-05-07 Identifier in Online Catalog: AAI9305522 OCLC Identifier: (UMI)AAI9305522
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