We fit the transmission data from patients within subgroups to the negative binomial distribution with mean R and dispersion parameter k, which characterizes individual variation in transmission, including the likelihood of superspreading events (i.

26) when the negative binomial distribution was fitted to data from large Ebola transmission chains in Guinea (32); this result suggests that the high variability assumption may be appropriate, but whether or not the assumption of high variability is an appropriate characterization for potential Ebola outbreaks in new countries is unclear.

The parameters a and b of the beta-binomial model can be chosen to provide flexibility to handle many possible situations in health services research that have this "probability" nature of constraining between 0 and 1, and are more diffuse than the over-dispersion capabilities of the negative

binomial distribution (Morris and Lock 2009).

The simulations were carried out by fitting unique negative binomial distributions to each player pairing in a side

For this reason, the negative binomial distribution (nbd) was deemed more appropriate than Poisson.

It seems intuitive to model the accident process by some classic count distribution such as the Poisson distribution because its interpretation is direct, as a limit of a

Binomial distribution with the number of tries going to infinity and the accident probability tending to 0.

Goodness-of-fit statistics for the lognormal, Poisson, and negative

binomial distributions were calculated for the four individual species and for all species to help judge which error structure best characterized the MRFSS catch-rate data.

The first term in Equation 4 is E(k), which, for the

binomial distribution, is n[p.

The binary statistic indicates p values for tests of

binomial distributions used to identify which answers were selected by students at levels above or below expected levels of 50% if students were randomly guessing at answers.

For example, the second moment restriction for binomial and negative

binomial distributions is

The

binomial distribution is then defined in terms of the proportion (y) of positive tows (r) to total tows (n) per cell, and the probability density function f(y) and associated variance Var (y) function are given by

Because a mixture of Lexis and Poisson variation may mimic a

binomial distribution (James 2000), it is invalid to infer from a seemingly

binomial distribution that the probability of a male birth is equal at all trials.