In probability theory, a "'beta negative binomial distribution "'is the probability distribution of a independent Bernoulli trials where the probability " p " of success on each trial is constant within any given experiment but is itself a random variable following a beta distribution, varying between different experiments.
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This is a special case of the class of generalized linear models which also contains specific forms of model capable of using the binomial distribution ( binomial regression, logistic regression ) or the negative binomial distribution where the assumptions of the Poisson model are violated, in particular when the range of count values is limited or when overdispersion is present.
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:: As a start, I would suggest having a look at negative binomial distribution-each " turn " would be a set of two independent ( up to the point where one dies, but that is irrelevant-" i think " ) Bernoulli trials with probability of'success'being the Hit value for that player.
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According to data collected in 1993 and 1994 during an outbreak in Alberta and the Northwest Territories, galled current-year shoots caused by spruce gall midge displayed a negative binomial distribution described by the mean " kp " = 5.3333, the variance " kpq " = 83.0828, and the dispersion parameter " k " = 0.3007.
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For example, in France and the UK, each month on average, 19 % of prices change ( 81 % are unchanged ), which implies that an average price spell lasts about 5.3 months ( the expected duration of a price spell is equal to the reciprocal of the frequency of price change if we interpret the empirical frequency as representing the Bernoulli probability of price change generating a negative binomial distribution of durations of price-spells ).
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:: ( e / c ) what you're talking about is a negative binomial distribution-the probability of getting m failures before getting n successes . in this case, n = 1 ( you are asking how many girls need to be born before a single boy is born ) and the mean for the NBD is n * p / ( 1-p ) = 1 * . 5 / . 5 = 1 . in realistic terms, half the time a boy will be born first, but in other cases progressively large numbers of girls need to be born before a boy arrives, balancing out the preponderance of only-child boys.
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