I asked your question to ChatGPT4 In statistics, what is the theta parameter of the negative binomial distribution?
The response contained some math symbols but I am sending in plain text mode so there may be some loss, hopefully not serious. The negative binomial distribution is used to model the number of successes before observing a fixed number of failures in a Bernoulli process. It has two parameters, typically denoted r and p: r - This is the number of failures until the experiment is stopped. p - This is the probability of success on any given trial. In some contexts, the negative binomial distribution is described in terms of the number of failures before a fixed number of successes. In this case: r would be the number of successes. p would still be the probability of success on any given trial. In some literature and software implementations, the negative binomial distribution's parameterization is provided in terms of r (or k) and θ instead of r and p. Here: r (or k) is the number of successes. θ represents a "success-to-failure" ratio. The relationship between p and θ is: p = θ / (θ+1) [i.e. p = theta / (theta + 1) ] Conversely, θ = p / (1−p) [i.e. theta = p / (1-p) ] In summary, θ is a parameter that captures the success-to-failure ratio in some parameterizations of the negative binomial distribution, and it can be related back to the success probability p. On Fri, Sep 15, 2023 at 5:06 AM Andrew Robinson via R-help <r-help@r-project.org> wrote: > > Hi John, > > the negative binomial is a tricky one - there are several different > parameterisations and therefore different interpretations of the parameters. > Joseph Hilbe wrote a whole book on it that might be wroth checking. > > Cheers, > > Andrew > > > -- > Andrew Robinson > Chief Executive Officer, CEBRA and Professor of Biosecurity, > School/s of BioSciences and Mathematics & Statistics > University of Melbourne, VIC 3010 Australia > Tel: (+61) 0403 138 955 > Email: a...@unimelb.edu.au > Website: https://researchers.ms.unimelb.edu.au/~apro@unimelb/ > > I acknowledge the Traditional Owners of the land I inhabit, and pay my > respects to their Elders. > On 15 Sep 2023 at 11:52 AM +1000, Sorkin, John <jsor...@som.umaryland.edu>, > wrote: > External email: Please exercise caution > > Colleagues, > > I want to use the power_NetativeBinomial function from the PASSED library. > The function requires a value for a parameter theta. The meaning of theta is > not given in the documentation (at least I can�t find it) of the function. > Further the descriptions of the negative binomial distribution that I am > familiar with do not mention theta as being a parameter of the distribution. > I noticed that when one runs the glm.nb function to perform a negative > binomial regression one obtains a value for theta. This leads to two questions > > 1. Is the theta required by the power_NetativeBinomial function the theta > that is produced by the glm.nb function > 2. What is theta, and how does it relate to the parameters of the negative > binomial distribution? > > Thank you, > John > > [[alternative HTML version deleted]] > > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.