In studying the occurrence of plants and animals in nature, the number of individuals may be counted in each of many equal units of space or time. The original counts can be summarized in a frequency distribution, showing the number of units containing x = 0, 1, 2, 3, ... individuals of a given species. If every unit in the series were exposed equally to the chance of containing the organism, the distribution would follow the Poisson series, each unit having the population mean as its expected frequency. It is easy to test whether the variation in the number of individuals per unit agrees with this hypothesis. Since the expected variance of a Poisson distribution is equal to its mean, the observed variance s2, multiplied by the degrees of freedom n, may be divided by the sample mean x to obtain x2 = ns2/x. More often than not x2 is significantly larger than its expectation, not only in distributions of plants and animals in nature but even in the laboratory. A number of distributions have been devised for series in which the variance is significantly larger than the mean (2, 11, 21), frequently on the basis of more or less complex biological models. In the present paper this characteristic will be called "over dispersion". Perhaps the first of these was the negative binomial, which arose in deriving the Poisson series from the point binomial (27, 32) although it had been formulated in 1714 (2). Comparisons of expected and observed distributions have shown its wide applicability to biological data. The relative ea-se with which the negative binomial can be computed and

Fitting the negative binomial distribution to biological data and note on the efficient fitting of the negative binomial

Recent research demonstrates that, the greater the number of previous spells of unemployment and the longer their duration, the more likely is the event that an individual will be unemployed at a point in time. Two explanations have been advanced to interpret this finding. The first is rooted in economic theory; the second is based solely on statistical considerations.

https://www.jstor.org/stable/pdfplus/2553150.pdf

Does Unemployment Cause Future Unemployment? Definitions, Questions and Answers from a Continuous Time Model of Heterogeneity and State Dependence.

Fitting the Negative Binomial Distribution to Biological Data

We examine how firms can create word-of-mouth peer influence and social contagion by designing viral features into their products and marketing campaigns. Word-of-mouth (WOM) is generally considered to be more effective at promoting product contagion when it is personalized and active. Unfortunately, the relative effectiveness of different viral features has not been quantified, nor has their effectiveness been definitively established, largely because of difficulties surrounding econometric identification of endogenous peer effects. We therefore designed a randomized field experiment on a popular social networking website to test the effectiveness of a range of viral messaging capabilities in creating peer influence and social contagion among the 1.4 million friends of 9,687 experimental users. Overall, we find that viral product design features can indeed generate econometrically identifiable peer influence and social contagion effects. More surprisingly, we find that passive-broadcast viral messaging generates a 246% increase in local peer influence and social contagion effects, while adding active-personalized viral messaging only generates an additional 98% increase in contagion. Although active-personalized messaging is more effective in encouraging adoption per message and is correlated with more user engagement and sustained product use, passive-broadcast messaging is used more often enough to eclipse those benefits, generating more total peer adoption in the network. In addition to estimating the effects of viral product design on social contagion and product diffusion, our work also provides a model for how randomized trials can be used to identify peer influence effects in networks.

https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID1879926_code110270.pdf?abstractid=1564856&mirid=1&type=2

Creating Social Contagion Through Viral Product Design: A Randomized Trial of Peer Influence in Networks

https://www.caee.utexas.edu/prof/kockelman/public_html/TRB07MVPLN.pdf

J. E. Kerrich

Papers

Accident statistics and the concept of accident-proneness