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The Cauchy Distribution
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The Cauchy Distribution
The Cauchy distribution can be used to model the distribution of
horizontal distances at which a line segment tilted at a random
angle cuts a line.
The Cauchy distribution has one scale parameter. The probability
density function is:
The Cauchy distribution looks similar to a normal distribution,
but has a much heavier tail. It can be used to study hypothesis
tests that assume a normal distribution. How well the tests perform
on data from a Cauchy distribution gives a good indication of the
sensitivity of the test to heavy-tail departures from
normality.
The mean and standard deviation of the Cauchy distribution are
undefined. This means that no amount of data points will yield a
more accurate or reliable estimate of the mean and standard
deviation than does a single point.
The Cauchy distribution is sometimes called the Lorentzian
distribution.
The Cauchy distribution is implemented by the CauchyDistribution
class. It has one constructor which takes the scale parameter as
its only parameter. The following constructs a beta distribution
with scale parameter 3.2:
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CauchyDistribution cauchy = new CauchyDistribution(3.2); |
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Dim cauchy As ChiSquareDistribution = New (3.2) |
The CauchyDistribution class has one specific
property,
ScaleParameter, that returns the scale parameter of
the distribution.
CauchyDistribution 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 = CauchyDistribution.GetRandomVariate(random, 3.2); |
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Dim random As MersenneTwister = New MersenneTwister()
Dim variate As Double = CauchyDistribution.GetRandomVariate(random, 3.2) |
For details of the properties and methods common to all
continuous distribution classes, see the topic on ContinuousDistribution
class.
Up: Continuous Probability Distributions Next: The Chi-Square Distribution Previous: The Beta Distribution Contents
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