Hyperbolic distribution

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Overview

Continuous probability distribution Probability density function Hyperbola Normal distribution Financial assets

10 related topics

Key facts & relationships

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Mean: μ + δ β K 2 ( δ γ ) γ K 1 ( δ γ ) {\displaystyle \mu +{\frac {\delta \beta K_{2}(\delta \gamma )}{\gamma K_{1}(\delta \gamma )}}}
MGF: e μ z γ K 1 ( δ ( α 2 − ( β + z ) 2 ) ) ( α 2 − ( β + z ) 2 ) K 1 ( δ γ ) {\displaystyle {\frac {e^{\mu z}\gamma K_{1}(\delta {\sqrt {(\alpha ^{2}-(\beta +z)^{2})}})}{{\sqrt {(\…
Mode: μ + δ β γ {\displaystyle \mu +{\frac {\delta \beta }{\gamma }}}
Parameters: μ {\displaystyle \mu } location (real) α {\displaystyle \alpha } (real) β {\displaystyle \beta } asymmetry parameter (real) δ {\displaystyle \delta } scale parameter (real) γ =…
PDF: γ 2 α δ K 1 ( δ γ ) e − α δ 2 + ( x − μ ) 2 + β ( x − μ ) {\displaystyle {\frac {\gamma }{2\alpha \delta K_{1}(\delta \gamma )}}\;e^{-\alpha {\sqrt {\delta ^{2}+(x-\mu )^{2}}}+\…
Support: x ∈ ( − ∞ , + ∞ ) {\displaystyle x\in (-\infty ,+\infty )\!}

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Overview

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Map overview Semantic statistics

Nodes12

Edges11

Triples9

Avg. degree1.83

Density0.166667

Components1

How this topic connects Entity context

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Hyperbolic distribution

Top relations

is a · 2

Hyperbolic distribution → continuous probability distribution characterized by the logarithm of the probability density function being a hyperbola, random mixture of normal distributions

Mean · 1

Hyperbolic distribution → μ + δ β K 2 ( δ γ ) γ K 1 ( δ γ ) {\displaystyle \mu +{\frac {\delta \beta K_{2}(\delta \gamma )}{\gamma K_{1}(\delta \gamma )}}}

MGF · 1

Hyperbolic distribution → e μ z γ K 1 ( δ ( α 2 − ( β + z ) 2 ) ) ( α 2 − ( β + z ) 2 ) K 1 ( δ γ ) {\displaystyle {\frac {e^{\mu z}\gamma K_{1}(\delta {\sqrt {(\alpha ^{2}-(\beta +z)^{2})}})}{{\sqrt {(\…

Mode · 1

Hyperbolic distribution → μ + δ β γ {\displaystyle \mu +{\frac {\delta \beta }{\gamma }}}

Parameters · 1

Hyperbolic distribution → μ {\displaystyle \mu } location (real) α {\displaystyle \alpha } (real) β {\displaystyle \beta } asymmetry parameter (real) δ {\displaystyle \delta } scale parameter (real) γ =…

PDF · 1

Hyperbolic distribution → γ 2 α δ K 1 ( δ γ ) e − α δ 2 + ( x − μ ) 2 + β ( x − μ ) {\displaystyle {\frac {\gamma }{2\alpha \delta K_{1}(\delta \gamma )}}\;e^{-\alpha {\sqrt {\delta ^{2}+(x-\mu )^{2}}}+\…

Support · 1

Hyperbolic distribution → x ∈ ( − ∞ , + ∞ ) {\displaystyle x\in (-\infty ,+\infty )\!}

Variance · 1

Hyperbolic distribution → δ K 2 ( δ γ ) γ K 1 ( δ γ ) + β 2 δ 2 γ 2 ( K 3 ( δ γ ) K 1 ( δ γ ) − K 2 2 ( δ γ ) K 1 2 ( δ γ ) ) {\displaystyle {\frac {\delta K_{2}(\delta \gamma )}{\gamma K_{1}(\delta \gam…

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Important terminology

distribution hyperbolic normal hyperbola logarithm distributions form generalised observation function turbulent continuous probability characterized density thus decreases exponentially slowly therefore

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
Hyperbolic distribution	Mean	μ + δ β K 2 ( δ γ ) γ K 1 ( δ γ ) {\displaystyle \mu +{\frac {\delta \beta K_{2}(\delta \gamma )}{\gamma K_{1}(\delta \gamma )}}}	1.00	infobox
Hyperbolic distribution	MGF	e μ z γ K 1 ( δ ( α 2 − ( β + z ) 2 ) ) ( α 2 − ( β + z ) 2 ) K 1 ( δ γ ) {\displaystyle {\frac {e^{\mu z}\gamma K_{1}(\delta {\sqrt {(\alpha ^{2}-(\beta +z)^{2})}})}{{\sqrt {(\…	1.00	infobox
Hyperbolic distribution	Mode	μ + δ β γ {\displaystyle \mu +{\frac {\delta \beta }{\gamma }}}	1.00	infobox
Hyperbolic distribution	Parameters	μ {\displaystyle \mu } location (real) α {\displaystyle \alpha } (real) β {\displaystyle \beta } asymmetry parameter (real) δ {\displaystyle \delta } scale parameter (real) γ =…	1.00	infobox
Hyperbolic distribution	PDF	γ 2 α δ K 1 ( δ γ ) e − α δ 2 + ( x − μ ) 2 + β ( x − μ ) {\displaystyle {\frac {\gamma }{2\alpha \delta K_{1}(\delta \gamma )}}\;e^{-\alpha {\sqrt {\delta ^{2}+(x-\mu )^{2}}}+\…	1.00	infobox
Hyperbolic distribution	Support	x ∈ ( − ∞ , + ∞ ) {\displaystyle x\in (-\infty ,+\infty )\!}	1.00	infobox
Hyperbolic distribution	Variance	δ K 2 ( δ γ ) γ K 1 ( δ γ ) + β 2 δ 2 γ 2 ( K 3 ( δ γ ) K 1 ( δ γ ) − K 2 2 ( δ γ ) K 1 2 ( δ γ ) ) {\displaystyle {\frac {\delta K_{2}(\delta \gamma )}{\gamma K_{1}(\delta \gam…	1.00	infobox
Hyperbolic distribution	is a	continuous probability distribution characterized by the logarithm of the probability density function being a hyperbola	0.90	text
Hyperbolic distribution	is a	random mixture of normal distributions	0.90	text

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