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The Geometric Distribution
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The Geometric Distribution
The geometric distribution is a special case of the negative binomial
distribution. It models the number of failures before the first
success in a series of Bernoulli trials. A Bernoulli trial is an
experiment with two possible outcomes, labeled 'success' and
'failure,' where the probability of success has a fixed value for
all trials.
The geometric distribution has one parameter, p, that
specifies the probability of success.
Examples of the geometric distribution are:
- The number of successive hits by a baseball
player (assuming the probability of a hit is constant) has a
geometric distribution with parameter p = 1 - (batting
average).
- The number of attempts made by a player to hit a target has a
geometric distribution.
The geometric distribution is implemented by the
GeometricDistribution class. It has one constructor
which has one parameter: the probability of success of a trial. The
probability must be between 0 and 1. The following constructs a
geometric distribution with probability of success 0.4:
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GeometricDistribution geometric = new GeometricDistribution(0.4); |
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Dim geometric As GeometricDistribution = New GeometricDistribution(0.4) |
The GeometricDistribution class has one specific
property,
ProbabilityOfSuccess, which returns the probabiltiy of
success of a trial.
GeometricDistribution has one static
(Shared in Visual Basic) method,
GetRandomVariate, which generates a random variate
using a user-supplied uniform random number generator.
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MersenneTwister random = new MersenneTwister();
double variate = GeometricDistribution.GetRandomVariate(random, 0.4); |
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Dim random As MersenneTwister = New MersenneTwister()
Dim variate As Double = GeometricDistribution.GetRandomVariate(random, 0.4) |
The above example uses the Mersenne
Twister to generate uniform random numbers.
For details of the properties and methods common to all discrete
probability distribution classes, see the topic on DiscreteDistribution
class.
Up: Discrete Probability Distributions Next: The Hypergeometric Distribution Previous: The Binomial Distribution Contents
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