Holtsmark distribution

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Characteristic function

Characteristic function Location parameter Scale parameter Mean Median

8 related topics

Probability density function

Probability distribution Normal Cauchy Lévy distributions Gamma function

5 related topics

Overview

Continuous probability distribution Stable distribution Skewness Probability density function Elementary functions

7 related topics

Key facts & relationships

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CF: exp ⁡ [ i t μ − | c t | 3 / 2 ] {\displaystyle \exp \left[~it\mu \!-\!|ct|^{3/2}~\right]}
Excess kurtosis: undefined
Mean: μ
Median: μ
MGF: undefined
Mode: μ

Topics to explore

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Overview

Continuous probability distribution
Stable distribution
Skewness
Probability density function
Elementary functions
Hypergeometric functions Generalized hypergeometric function
Johan Peter Holtsmark

Characteristic function

Characteristic function Characteristic function (probability theory)
Location parameter
Scale parameter
Mean
Median
Mode Mode (statistics)
Variance
Moments Moment (mathematics)

Probability density function

Probability distribution
Normal Normal distribution
Cauchy Cauchy distribution
Lévy distributions Lévy distribution
Gamma function

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Map overview Semantic statistics

Nodes24

Edges23

Triples14

Avg. degree1.92

Density0.083333

Components1

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Holtsmark distribution

Top relations

is a · 3

Holtsmark distribution → continuous probability distribution, special case of a stable distribution with the index of stability or shape parameter α, stable distribution with α

CF · 1

Holtsmark distribution → exp ⁡ [ i t μ − | c t | 3 / 2 ] {\displaystyle \exp \left[~it\mu \!-\!|ct|^{3/2}~\right]}

Excess kurtosis · 1

Holtsmark distribution → undefined

Mean · 1

Holtsmark distribution → μ

Median · 1

Holtsmark distribution → μ

MGF · 1

Holtsmark distribution → undefined

Mode · 1

Holtsmark distribution → μ

Parameters · 1

Holtsmark distribution → c ∈ (0, ∞) — scale parameter μ ∈ (−∞, ∞) — location parameter

PDF · 1

Holtsmark distribution → expressible in terms of hypergeometric functions; see text

Skewness · 1

Holtsmark distribution → undefined

Important terminology Word statistics

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Important terminology

distribution holtsmark displaystyle function probability stable density functions since left right parameter distributions mu symmetric terms hypergeometric one closed form

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
Holtsmark distribution	CF	exp ⁡ [ i t μ − \| c t \| 3 / 2 ] {\displaystyle \exp \left[~it\mu \!-\!\|ct\|^{3/2}~\right]}	1.00	infobox
Holtsmark distribution	Excess kurtosis	undefined	1.00	infobox
Holtsmark distribution	Mean	μ	1.00	infobox
Holtsmark distribution	Median	μ	1.00	infobox
Holtsmark distribution	MGF	undefined	1.00	infobox
Holtsmark distribution	Mode	μ	1.00	infobox
Holtsmark distribution	Parameters	c ∈ (0, ∞) — scale parameter μ ∈ (−∞, ∞) — location parameter	1.00	infobox
Holtsmark distribution	PDF	expressible in terms of hypergeometric functions; see text	1.00	infobox
Holtsmark distribution	Skewness	undefined	1.00	infobox
Holtsmark distribution	Support	x ∈ R	1.00	infobox
Holtsmark distribution	Variance	infinite	1.00	infobox
Holtsmark distribution	is a	continuous probability distribution	0.90	text
Holtsmark distribution	is a	special case of a stable distribution with the index of stability or shape parameter α	0.90	text
Holtsmark distribution	is a	stable distribution with α	0.90	text

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