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Approaches to stochastic modeling; Estimating and testing stochastic models; Brand-choice models; Zero-order models; Two state markov models; Linear learning models for brand choice; A probability diffusion model; Application of the probability diffusion model; Purchase incidence models; Models for purchase timing and market penetration; A stochastic model for monitoring new product adoption; Parameter estimations and some emperical results for STEAM; Extension to STEAM.
This book is about marketing models and the process of model building. Our primary focus is on models that can be used by managers to support marketing decisions. It has long been known that simple models usually outperform judgments in predicting outcomes in a wide variety of contexts. For example, models of judgments tend to provide better forecasts of the outcomes than the judgments themselves (because the model eliminates the noise in judgments). And since judgments never fully reflect the complexities of the many forces that influence outcomes, it is easy to see why models of actual outcomes should be very attractive to (marketing) decision makers. Thus, appropriately constructed models can provide insights about structural relations between marketing variables. Since models explicate the relations, both the process of model building and the model that ultimately results can improve the quality of marketing decisions. Managers often use rules of thumb for decisions. For example, a brand manager will have defined a specific set of alternative brands as the competitive set within a product category. Usually this set is based on perceived similarities in brand characteristics, advertising messages, etc. If a new marketing initiative occurs for one of the other brands, the brand manager will have a strong inclination to react. The reaction is partly based on the manager's desire to maintain some competitive parity in the mar keting variables.
This book presents an algebraic development of the theory of countable state space Markov chains with discrete- and continuous-time parameters. A Markov chain is a stochastic process characterized by the Markov prop erty that the distribution of future depends only on the current state, not on the whole history. Despite its simple form of dependency, the Markov property has enabled us to develop a rich system of concepts and theorems and to derive many results that are useful in applications. In fact, the areas that can be modeled, with varying degrees of success, by Markov chains are vast and are still expanding. The aim of this book is a discussion of the time-dependent behavior, called the transient behavior, of Markov chains. From the practical point of view, when modeling a stochastic system by a Markov chain, there are many instances in which time-limiting results such as stationary distributions have no meaning. Or, even when the stationary distribution is of some importance, it is often dangerous to use the stationary result alone without knowing the transient behavior of the Markov chain. Not many books have paid much attention to this topic, despite its obvious importance.
Quantitative marketing has been gaining importance during the last decade. This is indicated by the growing number of model- and method-oriented studies published in leading journals as well as by the many successful applications of quantitative approaches in pricing, advertising, new product planning, and market segmentation decisions. In addition, market research has clearly benefitted from applying advanced quantitative models and methods in practice. Some 60 researchers – among them worldwide leading scholars – offer a broad overview of quantitative approaches in marketing. They not only highlight diverse mathematical and methodological perspectives, but also demonstrate the relevance and practical consequences of applying quantitative approaches to marketing problems.
An Introduction to Stochastic Modeling provides information pertinent to the standard concepts and methods of stochastic modeling. This book presents the rich diversity of applications of stochastic processes in the sciences. Organized into nine chapters, this book begins with an overview of diverse types of stochastic models, which predicts a set of possible outcomes weighed by their likelihoods or probabilities. This text then provides exercises in the applications of simple stochastic analysis to appropriate problems. Other chapters consider the study of general functions of independent, identically distributed, nonnegative random variables representing the successive intervals between renewals. This book discusses as well the numerous examples of Markov branching processes that arise naturally in various scientific disciplines. The final chapter deals with queueing models, which aid the design process by predicting system performance. This book is a valuable resource for students of engineering and management science. Engineers will also find this book useful.