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Voigt profile

The Voigt profile (named after Woldemar Voigt) is a probability distribution given by a convolution of a Cauchy-Lorentz distribution and a Gaussian distribution. It is often used in analyzing data from spectroscopy or diffraction.

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CDF
(complicated - see text)
CF
e − γ | t | − σ 2 t 2 / 2 {\displaystyle e^{-\gamma |t|-\sigma ^{2}t^{2}/2}}
Excess kurtosis
(not defined)
Mean
(not defined)
Median
0 {\displaystyle 0}
MGF
(not defined)

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Overview

Definition

History and applications

Properties

Voigt functions

Numeric approximations

Other related functions

Advanced semantic analysis

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Map overview Semantic statistics

Voigt profile

Nodes37
Edges36
Triples39
Avg. degree1.95
Density0.054054
Components1

How this topic connects Entity context

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Voigt profile

Top relations

related to history · 8
Voigt profile → Doppler, Due, Faddeeva, Gaussian, In, Lorentzian, Voigt, Waldemar Voigt
related to Properties · 6
Voigt profile → Cauchy, It, The, The Lorentzian, The Voigt, Voigt
related to The width of the Voigt profile · 6
Voigt profile → FWHM, Gaussian, Lorentzian, The, The FWHM, Voigt
related to Pseudo-Voigt approximation · 4
Voigt profile → Gaussian, Lorentzian, The, Voigt
related to Definition · 3
Voigt profile → Gaussian, The Voigt, Without
CDF · 1
Voigt profile → (complicated - see text)
CF · 1
Voigt profile → e − γ | t | − σ 2 t 2 / 2 {\displaystyle e^{-\gamma |t|-\sigma ^{2}t^{2}/2}}
Excess kurtosis · 1
Voigt profile → (not defined)
Mean · 1
Voigt profile → (not defined)
Median · 1
Voigt profile → 0 {\displaystyle 0}

Important terminology Word statistics

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Important terminology

function displaystyle voigt profile gaussian convolution width distribution lorentzian gamma sigma derivatives profiles line centered pseudo-voigt approximation spectroscopy given used

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Voigt profileCDF(complicated - see text)1.00infobox
Voigt profileCFe − γ | t | − σ 2 t 2 / 2 {\displaystyle e^{-\gamma |t|-\sigma ^{2}t^{2}/2}}1.00infobox
Voigt profileExcess kurtosis(not defined)1.00infobox
Voigt profileMean(not defined)1.00infobox
Voigt profileMedian0 {\displaystyle 0}1.00infobox
Voigt profileMGF(not defined)1.00infobox
Voigt profileMode0 {\displaystyle 0}1.00infobox
Voigt profileParametersγ , σ > 0 {\displaystyle \gamma ,\sigma >0}1.00infobox
Voigt profilePDFℜ [ w ( z ) ] σ 2 π , z = x + i γ σ 2 {\displaystyle {\frac {\Re [w(z)]}{\sigma {\sqrt {2\pi }}}},~~~z={\frac {x+i\gamma }{\sigma {\sqrt {2}}}}}1.00infobox
Voigt profileSkewness(not defined)1.00infobox
Voigt profileSupportx ∈ ( − ∞ , ∞ ) {\displaystyle x\in (-\infty ,\infty )}1.00infobox
Voigt profileVariance(not defined)1.00infobox

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    Min side: 3
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