I am trying to model the number a goals scored by the teams of a soccer tournament at group stage. The tournament involves eight groups of four teams each. This means that each group involves 6 games and therefore there is a total frequency of 96 determined a priori. However there is an observed over-dispersion. Poisson distribution fit hypothesis is therefore dropped in preference for a negative binomial fit hypothesis. My problem is how to compute the expected frequencies under the negative binomial fit. I need assistance.
did you say the expectation of a negative binomial random variable?
if it is you can compute by expec. = n*r / (1-p).
where p is the rate of success, and n is the number of trials, r is the number of failures
I hope to be helpful,
I am not using any statistical package. Negative binomial distribution is like this: Bernoulli trials each with probability p of success are taken until the rth success occurs. The number r of successes is fixed but X the number of failures is a random variable. The number of trials is therefore a random variable. How do I apply this to my problem to obtain the expected frequencies? What does the total frequency of 96 from 48 soccer games represent within this context?
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