Bates distribution

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Extensions and Applications

Normal Gaussian distribution Shape-adjusting parameter Trapezoidal distribution Student-t distribution Long tail

12 related topics

Definition

Empirical mean Independent Probability density function Sign function

4 related topics

Overview

Probability Statistics Grace Bates Probability distribution Mean

13 related topics

Key facts & relationships

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CF: ( − i n ( e i b t n − e i a t n ) ( b − a ) t ) n {\displaystyle \left(-{\frac {in(e^{\tfrac {ibt}{n}}-e^{\tfrac {iat}{n}})}{(b-a)t}}\right)^{n}}
Excess kurtosis: − 6 5 n {\displaystyle -{\tfrac {6}{5n}}}
Mean: 1 2 ( a + b ) {\displaystyle {\tfrac {1}{2}}(a+b)}
Parameters: − ∞ < a < b < ∞ {\displaystyle -\infty <a<b<\infty } n ≥ 1 {\displaystyle n\geq 1} integer
PDF: see below
Skewness: 0

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Map overview Semantic statistics

Nodes33

Edges32

Triples17

Avg. degree1.94

Density0.060606

Components1

How this topic connects Entity context

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Bates distribution

Top relations

has application · 7

Bates distribution → Bates, By, Gaussian, Replacing, Then, Thus, With

related to Definition · 2

Bates distribution → The, The Bates

CF · 1

Bates distribution → ( − i n ( e i b t n − e i a t n ) ( b − a ) t ) n {\displaystyle \left(-{\frac {in(e^{\tfrac {ibt}{n}}-e^{\tfrac {iat}{n}})}{(b-a)t}}\right)^{n}}

Excess kurtosis · 1

Bates distribution → − 6 5 n {\displaystyle -{\tfrac {6}{5n}}}

Mean · 1

Bates distribution → 1 2 ( a + b ) {\displaystyle {\tfrac {1}{2}}(a+b)}

Parameters · 1

Bates distribution → − ∞ a b ∞ {\displaystyle -\infty ab\infty } n ≥ 1 {\displaystyle n\geq 1} integer

PDF · 1

Bates distribution → see below

Skewness · 1

Bates distribution → 0

Support · 1

Bates distribution → x ∈ [ a , b ] {\displaystyle x\in [a,b]}

Variance · 1

Bates distribution → 1 12 n ( b − a ) 2 {\displaystyle {\tfrac {1}{12n}}(b-a)^{2}}

Important terminology Word statistics

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Important terminology

distribution displaystyle bates mean interval unit independent uniform probability uniformly distributed random variables parameter normal triangular function gaussian irwin-hall also

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
Bates distribution	CF	( − i n ( e i b t n − e i a t n ) ( b − a ) t ) n {\displaystyle \left(-{\frac {in(e^{\tfrac {ibt}{n}}-e^{\tfrac {iat}{n}})}{(b-a)t}}\right)^{n}}	1.00	infobox
Bates distribution	Excess kurtosis	− 6 5 n {\displaystyle -{\tfrac {6}{5n}}}	1.00	infobox
Bates distribution	Mean	1 2 ( a + b ) {\displaystyle {\tfrac {1}{2}}(a+b)}	1.00	infobox
Bates distribution	Parameters	− ∞ < a < b < ∞ {\displaystyle -\infty <a<b<\infty } n ≥ 1 {\displaystyle n\geq 1} integer	1.00	infobox
Bates distribution	PDF	see below	1.00	infobox
Bates distribution	Skewness	0	1.00	infobox
Bates distribution	Support	x ∈ [ a , b ] {\displaystyle x\in [a,b]}	1.00	infobox
Bates distribution	Variance	1 12 n ( b − a ) 2 {\displaystyle {\tfrac {1}{12n}}(b-a)^{2}}	1.00	infobox
Bates distribution	has application	With	0.60	section
Bates distribution	has application	Bates	0.60	section
Bates distribution	has application	Gaussian	0.60	section
Bates distribution	has application	Replacing	0.60	section

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