In recent years, the model of Bass [1] has been one of the main references in models of adopting timing of innovations. From this model, Bemmaor [2] formulated a derivation for which the individual-level model of adopting timing of a new product is randomly distributed according to the shifted Gompertz distribution.
Let X be a random variable having the shifted Gompertz distribution with parameters α and β, denoted by SG(α,β), where α > 0 is a shape parameter and β > 0 is a scale parameter. The probability density function (PDF) of X is