Negative binomial

What Negative binomial is

Negative binomial is a type of distribution used to model the probability of a given number of successes in a sequence of independent Bernoulli trials (i.e. events with only two possible outcomes). This type of distribution is often used in statistical tests to analyze the probability of a certain number of successes in a given number of trials.

Steps for Negative Binomial:

  1. Define the number of trials: The first step in using the negative binomial distribution is to define the number of trials that will be conducted. This will determine the shape of the distribution, as the probability of any given number of successes will be affected by the number of trials.

  2. Define the probability of success: The second step is to define the probability of success for each Bernoulli trial. This probability will determine the shape of the distribution, as it will affect the probability of any given number of successes.

  3. Calculate the probability of a given number of successes: The third step is to calculate the probability of a given number of successes in the given number of trials. This can be done by using the probability mass function of the negative binomial distribution.

  4. Interpret the results: The final step is to interpret the results. This can be done by analyzing the shape of the distribution and the probability of any given number of successes. The interpretation of the results will depend on the context in which the negative binomial distribution is being used.

Examples

  1. Counting the number of failures before a specified number of successes in repeated Bernoulli trials.
  2. Modeling the number of times an event needs to occur before a given number of failures occur.
  3. Estimating the probability of a given number of failures before a given number of successes in repeated Bernoulli trials.
  4. Modeling the number of times an event needs to occur before a given number of successes occur.
  5. Estimating the probability of a given number of successes before a given number of failures in repeated Bernoulli trials.
  6. Modeling the number of times an event needs to occur before a given number of successes or failures occur.
  7. Estimating the probability of a given number of successes or failures before a given number of successes or failures in repeated Bernoulli trials.

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