Statistics and Probability Glossary
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Negative Binomial Experiment
A negative binomial experiment is a
statistical experiment
that has the following properties:
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The experiment consists of x repeated trials.
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Each trial can result in just two possible outcomes. We call one of these
outcomes a success and the other, a failure.
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The probability of success, denoted by p, is the same on every
trial.
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The trials are independent;
that is, the outcome on one trial does not affect the outcome on other trials.
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The experiment continues until r successes are observed, where r
is specified in advance.
Consider the following statistical experiment. You flip a coin repeatedly and count
the number of times the coin lands on heads. You continue flipping the coin until
it has landed 5 times on heads. This is a negative binomial experiment
because:
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The experiment consists of repeated trials. We flip a coin repeatedly until it
has landed 5 times on heads.
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Each trial can result in just two possible outcomes - heads or tails.
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The probability of success is constant - 0.5 on every trial.
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The trials are independent; that is, getting heads on one trial does not affect
whether we get heads on other trials.
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The experiment continues until a fixed number of successes have occurred;
in this case, 5 heads.
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