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CauchyDistribution

CauchyDistribution[a, b]
represents a Cauchy distribution with location parameter a and scale parameter b.
  • The probability density for value x in a Cauchy distribution is proportional to . »
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Basic Examples   (2)
The mean and variance of a Cauchy distribution are indeterminate:
Probability density function:
The mean and variance of a Cauchy distribution are indeterminate:
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Probability density function:
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Scope   (3)
Generate a set of pseudorandom numbers that are Cauchy distributed:
Higher-order moments are also indeterminate:
The q^(th) quantile of a Cauchy distribution:
Applications   (2)
Plot the cumulative distribution function of the random variable:
A contour plot as both x and b are varied:
Properties & Relations   (2)
The probability density function integrates to unity:
CauchyDistribution[0, 1] is equivalent to StudentTDistribution with nu=1:
Possible Issues   (2)
CauchyDistribution is not defined when a is nonreal:
CauchyDistribution is not defined when b is non-positive:
Substitution of invalid parameters into symbolic outputs gives results that are not meaningful:
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