What is negative binomial distribution used for?

What is negative binomial distribution used for?

The negative binomial distribution is a probability distribution that is used with discrete random variables. This type of distribution concerns the number of trials that must occur in order to have a predetermined number of successes.

Can a binomial random variable be negative?

A negative binomial random variable is the number X of repeated trials to produce r successes in a negative binomial experiment. The probability distribution of a negative binomial random variable is called a negative binomial distribution. The negative binomial distribution is also known as the Pascal distribution.

How do you know if a binomial is negative?

Negative Binomial Experiment / Distribution: Definition, Examples

1. Fixed number of n trials.
2. Each trial is independent.
3. Only two outcomes are possible (Success and Failure).
4. Probability of success (p) for each trial is constant.
5. A random variable Y= the number of successes.

Is the negative binomial a gamma or Poisson distribution?

Gamma–Poisson mixture. That is, we can view the negative binomial as a Poisson (λ) distribution, where λ is itself a random variable, distributed as a gamma distribution with shape = r and scale θ = p/ (1 − p) or correspondingly rate β = (1 − p)/p .

Can a gamma-Poisson be converted into an exponential?

Now, a gamma-poisson is a “stretched” poisson with a larger variance. A Weibull distribution is a “stretched” exponential with a larger variance. But can these two be easily converted into each other, in the same way Poisson can be converted into exponential?

Can a gamma Poisson be converted to a Weibull distribution?

One can convert one distribution into the other, depending on whether it is easier to model events or times. Now, a gamma-poisson is a “stretched” poisson with a larger variance. A Weibull distribution is a “stretched” exponential with a larger variance.

Is the variance of a gamma mixture greater than its mean?

However, if we place a gamma prior on θ, and then marginalize out θ, we get a negative binomial (NB) distribution, which has the useful property that its variance can be greater than its mean. The derivation is