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[(1 - p)/(1 - pet)]r for t < -ln(p)

where

p = probability of success in each trial,

r = number of failures before success.

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Q: Moment generating function of a negative binomial distribution?
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What are mean and variance of negative binomial distribution by conclusion?

what is meant by a negative binomial distribution what is meant by a negative binomial distribution


How you can use negative binomial distribution in everyday life?

The negative binomial can be applied in any situation in which there is a series of independent trials, each of which can result in either of just two outcomes. The distribution applies to the number of trials that occur before the designated outcome occurs. For example, if you start flipping a fair coin repeatedly the negative binomial distribution gives the number of times you must flip the coin until you see 'heads'. There are also 'everyday' applications in inventory control and the insurance industry. Please see the link.


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Nothing really. It concerns an experiment with identified success and failure probabilities (p and q), or Bernoulli trials, like the conventional binomial distribution. In an negative binomial experiment, the experiment is stopped after "r" successes occur in n trials. Thus, there must be r-1 successes in the first n-1 trials, and the final trial must be a success. This stopping event causes a n-1 and r-1 terms to appear in the factorial expressions of the distribution, which I suspect is the origins of calling this distribution a "negative binomial distribution." I would prefer to call this a Bernoulli experiment distibution with a stopping rule, but that's probably much too long. Some excellent websites provide examples and more discussion: http://mathworld.wolfram.com/NegativeBinomialDistribution.html http://stattrek.com/Lesson2/NegBinomial.aspx http://en.wikipedia.org/wiki/Negative_binomial_distribution Stattrek has very good examples. Note the distribution can be expressed in a number of forms.


Can the F distribution be negative?

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Define binomial theorem?

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Can the expected value of a discrete probability distribution be negative?

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Is Sin a negative function or positive?

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