A Generalized Logistic Function with an Application to the Effect of Advertising

Abstract A generalization of the common logistic function is developed, incorporating a non-unit saturation level, a non-zero intercept, and a non-symmetric shape. The dependence of the three generalized characteristics on (estimated) parameter values is exhibited. The statistical properties of the function are developed for the case where the dependent variable is a relative frequency. An empirical application shows that the effect of advertising on market share is best depicted by a curve which is everywhere concave to the origin.