HyperbolicDistribution

HyperbolicDistribution[, , , ]
represents a hyperbolic distribution with location parameter , scale parameter , shape parameter , and skewness parameter .

HyperbolicDistribution[, , , , ]
represents a generalized hyperbolic distribution with shape parameter .

DetailsDetails

  • The probability density for value in a hyperbolic distribution is proportional to .
  • The probability density for value in a generalized hyperbolic distribution is proportional to  ⅇ^(beta (x-mu))sqrt(delta^2+(x-mu)^2)^(lambda-1/2) TemplateBox[{{lambda, -, {1, /, 2}}, {alpha,  , {sqrt(, {{delta, ^, 2}, +, {{(, {x, -, mu}, )}, ^, 2}}, )}}}, BesselK].
  • HyperbolicDistribution allows and to be any positive real number, and any real number, and such that .
  • HyperbolicDistribution can be used with such functions as Mean, CDF, and RandomVariate.

ExamplesExamplesopen allclose all

Basic Examples (6)Basic Examples (6)

Probability density function of a hyperbolic distribution:

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Cumulative distribution function of a hyperbolic distribution:

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Mean and variance of a hyperbolic distribution:

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Probability density function of a generalized hyperbolic distribution:

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Cumulative distribution function of a generalized hyperbolic distribution:

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Mean and variance of a generalized hyperbolic distribution:

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