To beat Barry Bond's record of 73 home runs in a single season, the number of times he would need to be at bat would be given by The number of times he shoplifts and gets away with it before being thrown in jail is given byĪ certain baseball player hits a home run for every 12 times he is at bat. Note: The identifier abbreviates Binom so as to keep the identifier below 20 characters total.Ī shoplifter has a 20% change of getting caught and convicted each time he commits the crime (hence, his probability of success is 80%). This computes the value «k» such that the probability of a value sampled from a NegativeBinomial(r, p) distribution has a value of «k» or less is «u». The inverse of the CumNegativeBinomial(k, r, p) function. Turning this around, if you are trying to decide which of the discrete distributions to use to describe an uncertain quantity and all you have is the first two moments, then you can chose between these three distributions based on whether the variance is less than, equal to, or greater than the mean. For the Binomial distribution the variance is less than the mean, for the Poisson they are equal, and for the NegativeBinomial distribution the variance is greater than the mean. ![]() If we characterize discrete distributions according to the first two moments - specifically how the variance compares to the mean - then three distributions span the space of possibilities. ![]() The NegativeBinomial distribution can be considered to be one of the three basic discrete distributions on the non-negative integers, with Poisson and Binomial being the other two. The sample values are non-negative integers. ![]() The negative binomial distribution is a discrete probability distribution that models the number of successes that occur before «r» failures, where each independent trial is a success with probability «p».
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