ABSTRACT
In this chapter, the author turns to a question which concerns a series of observations expressed over time, termed a time series. Evaluating choices over time implies studying competition between alternates. The author discusses the mathematical properties of a competitive Binomial system undergoing simple continuous change over time, before considering more complex systems. Neologisms may die out as fast as they spread, for example, if they are driven out by other, new alternates. If more than two alternate forms are competing, behaviour may be more complex because two forms may be increasing in usage at the same time. In summary, the logistic scale provides a model of competition over time within a system as linear change bounded probabilistically. Regression methods find the closest match between an observed set of data and a function, such as a straight line, a polynomial, a power curve or, in this case, an S-curve.
