What Is a Negative Binomial Distribution Model?
A negative binomial distribution model is a probability distribution that is used to describe the number of successes in a series of independent and identical Bernoulli trials before a predetermined number of failures occur. In other words, the negative binomial distribution is used to model the probability of a certain number of successes occurring in a fixed number of trials. The negative binomial distribution model is a generalization of the geometric distribution. As such, the negative binomial distribution can be used to model a wide range of problems, including the number of successes in a series of Bernoulli trials before a predetermined number of failures occur, the number of successes in a series of Bernoulli trials before a predetermined number of successes occur, and the number of successes in a series of Bernoulli trials before a predetermined number of trials occur.
Examples of Negative Binomial Distribution Model
One example of a negative binomial distribution model is in the analysis of baseball statistics. For example, the number of home runs hit by a player in a given season can be modeled using a negative binomial distribution. In this case, the number of home runs hit by the player is the number of successes and the number of games played is the number of failures. Another example of a negative binomial distribution model is in the analysis of customer loyalty. In this case, the number of customers who remain loyal to a given company over a period of time can be modeled using a negative binomial distribution. In this case, the number of customers who remain loyal to the company is the number of successes and the number of customers who leave the company is the number of failures.
Conclusion
The negative binomial distribution model is a powerful tool for analyzing the probability of a certain number of successes occurring in a fixed number of trials. It can be used to model a wide range of problems, including the number of successes in a series of Bernoulli trials before a predetermined number of failures occur, the number of successes in a series of Bernoulli trials before a predetermined number of successes occur, and the number of successes in a series of Bernoulli trials before a predetermined number of trials occur. For further reading: