Failing firms and successful entrepreneurs: serial entrepreneurship as a temporal portfolio

Quoted in Sarasvathy (2000, p.14).

We abuse notation slightly in that we do not explicitly indicate the dependence of the p.m.f on the firm success probability. Also, there are a great many different equivalent formulae for the negative binomial; for a survey of the mess, see (Ross and Preece 1985). The above formulation may be found in (Feller 1968, section VI.8).

Typically, processes such as the Yule process, Polya urn processes, epidemic processes, etc. are pointed to, or specific distributions such as the Pareto, power law, negative binomial, Zipf’s law, etc. are held up as exemplars (Feller 1943; Greenwood and Udny 1920; Xekalaki 1983). The study of contagion originated in the classic analysis of industrial accidents by Greenwood and Yule (1920). Not only has much of the work on contagion remained confined to this literature, but contagion has usually been studied in the context of counting processes. While it is natural to think of contagion as an increase in the number of something or the other, it is also limiting in that it forces a frequentist flavor onto events that may be best described otherwise (for example, belief contagion). Growth is not to be confused with contagion. In the Polya urn, the number of marbles of either color is a non-decreasing function of time, but what makes the process contagious is the conditional increase in numbers.

The events, \( E(0),E(1), \ldots \) etc. are considered as the same event occurring at different time instants.