Geometric Distribution
Definition
The geometric pdf is
where q = 1 – p.
The geometric distribution is a special case of the negative
binomial distribution, with r = 1.
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Background
The geometric distribution is discrete, existing only on the
nonnegative integers. It is useful for modeling the runs of consecutive
successes (or failures) in repeated independent trials of a system.
The geometric distribution models the number of successes before
one failure in an independent succession of tests where each test
results in success or failure.
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Example
Suppose the probability of a five-year-old battery failing in
cold weather is 0.03. What is the probability of starting 25 consecutive
days during a long cold snap?
1 - geocdf(25,0.03)
ans =
0.4530
The plot shows the cdf for this scenario.
x = 0:25;
y = geocdf(x,0.03);
stairs(x,y)
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See Also
Discrete Distributions
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 | Generalized Pareto Distribution | | Hypergeometric Distribution |  |
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