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Probability density function  Plot of the centered Voigt profile for four cases. Each case has a full width at half-maximum of very nearly 3.6. The black and red profiles are the limiting cases of the Gaussian (γ =0) and the Lorentzian (σ =0) profiles respectively. | |||
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Cumulative distribution function  | |||
| Parameters | |||
|---|---|---|---|
| Support | |||
| CDF | (complicated - see text) | ||
| Mean | (not defined) | ||
| Median | |||
| Mode | |||
| Variance | (not defined) | ||
| Skewness | (not defined) | ||
| Excess kurtosis | (not defined) | ||
| MGF | (not defined) | ||
| CF | |||
![{\displaystyle {\frac {\Re [w(z)]}{\sigma {\sqrt {2\pi }}}},~~~z={\frac {x+i\gamma }{\sigma {\sqrt {2}}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d32b81cec7e6bba1f2c5ce2b2dbd4469531d9d53)
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.