Can binomial approximate hypergeometric distribution?
The exact probability distribution of X depends on whether the sampling is done with or without replacement. Its distribution is referred to as a hypergeometric distribution (Weiss 2010). In practice, however, a hyper-geometric distribution can usually be approximated by a binomial distribution.
What is beta binomial distribution used for?
The beta-binomial distribution is one of the simplest Bayesian models. It is widely used, including in epidemiology, intelligence testing and marketing. A distribution is beta-binomial if p, the probability of success, in a binomial distribution has a beta distribution with shape parameters α > 0 and β > 0.
Is the beta binomial distribution a conjugate prior for some sampling distribution?
The beta distribution is conjugate prior for the binomial distribution. Is the beta-binomial distribution a conjugate prior for some sampling distribution? You’re looking for the hypergeometric distribution. Incidentally, this link is one of the first two hits on Google for “beta binomial” “conjugate prior”.
Which is a conjugate prior for the hypergeometric distribution?
The beta-binomial distribution is a conjugate prior for the hypergeometric distribution. The following table describes four distributions related to the number of successes in a sequence of draws: The model of an urn with green and red marbles can be extended to the case where there are more than two colors of marbles.
How is the binomial distribution different from the hypergeometric distribution?
In contrast, the binomial distribution describes the probability of draws with replacement. The following conditions characterize the hypergeometric distribution: The result of each draw (the elements of the population being sampled) can be classified into one of two mutually exclusive categories (e.g. Pass/Fail or Employed/Unemployed).
What is the AIC for the beta binomial model?
The AIC for the competing binomial model is AIC = 25070.34 and thus we see that the beta-binomial model provides a superior fit to the data i.e. there is evidence for overdispersion.