negbis

negbis is a term that refers to a negative binomial distribution. This is a discrete probability distribution that describes the number of Bernoulli trials needed to achieve a fixed number of successes. A Bernoulli trial is an experiment with two possible outcomes, typically labeled "success" and "failure," where the probability of success is constant for each trial. The negative binomial distribution is characterized by two parameters: the number of successes (often denoted by r) and the probability of success in a single trial (often denoted by p).

There are two common parametrizations of the negative binomial distribution. One counts the number of failures before the r-th success, while the other counts the total number of trials until the r-th success. The choice of parametrization depends on the context of the problem being modeled. This distribution is frequently used in statistical modeling, particularly in fields such as biology, ecology, and finance, to model count data where overdispersion is present, meaning the variance is greater than the mean. For example, it can be used to model the number of accidents a person has before a certain number of injury-free periods, or the number of defective items found before a specified number of non-defective items.