Gaussian/Normal Distribution

Functions
template<typename T >
T	EGXMath::Gaussian (const T &x, const T &mu, const T &sigma)
	Gaussian function. The probability desnisty function of a normal distribution. \[ Gaussian(x)=\frac{1}{\sigma \sqrt{2\pi}}e^{\frac{-(x-\mu)^2}{2\sigma^2}} \] . More...
template<typename T >
T	EGXMath::NormalDistribution (const T &x, const T &mu, const T &sigma)
	Gaussian function. The probability desnisty function of a normal distribution. \[Gaussian(x)=\frac{1}{\sigma \sqrt{2\pi}}e^{\frac{-(x-\mu)^2}{2\sigma^2}}\] . More...
template<typename T >
T	EGXMath::GaussianFWHM (const T &sigma)
	Finds the full width half max (FWHM) of a gaussian/normal distribution. \[GaussianFWHM(x)=2\sqrt{2 ln 2} \sigma \] . More...
template<typename T >
T	EGXMath::NormalDistributionFWHM (const T &sigma)
	Finds the full width half max (FWHM) of a gaussian/normal distribution. \[GaussianFWHM(x)=2\sqrt{2 ln 2} \sigma \] . More...

Detailed Description

Function Documentation

Gaussian()

template<typename T >

T EGXMath::Gaussian	(	const T &	x,
		const T &	mu,
		const T &	sigma
	)

Gaussian function. The probability desnisty function of a normal distribution.

\[ Gaussian(x)=\frac{1}{\sigma \sqrt{2\pi}}e^{\frac{-(x-\mu)^2}{2\sigma^2}} \]

.

See http://mathworld.wolfram.com/GaussianFunction.html and http://mathworld.wolfram.com/NormalDistribution.html

Parameters

x	\(x\ (dimensionless)\) is the argument of the function.
mu	\(\mu\ (dimensionless)\) is the mean of the gaussian/normal distribution.
sigma	\(\sigma\ (dimensionless)\) is the standard deviation of the gaussian/normal distribution.

Returns

\(Gaussian(x)\ (dimensionless)\) the value of the gaussian/normal distribution at x.

See also

NormalDistribution() for alias.

GaussianFWHM() for full width half max of gaussian/normal distribution.

NormalDistributionFWHM() for full width half max of gaussian/normal distribution.

GaussianFWHM()

template<typename T >

T EGXMath::GaussianFWHM

(

const T &

sigma

)

Finds the full width half max (FWHM) of a gaussian/normal distribution.

\[GaussianFWHM(x)=2\sqrt{2 ln 2} \sigma \]

.

See http://mathworld.wolfram.com/GaussianFunction.html and http://mathworld.wolfram.com/NormalDistribution.html

Parameters

sigma

\(\sigma\ (dimensionless)\) is the standard deviation of the gaussian/normal distribution.

Returns

\(GaussianFWHM(x)\ (dimensionless)\) the full width half max of gaussian/normalDistribution.

See also

Gaussian() for gaussian/normal distribution.

NormalDistribution() for gaussian/normal distribution.

NormalDistributionFWHM() for alias.

NormalDistribution()

template<typename T >

T EGXMath::NormalDistribution	(	const T &	x,
		const T &	mu,
		const T &	sigma
	)

Gaussian function. The probability desnisty function of a normal distribution.

\[Gaussian(x)=\frac{1}{\sigma \sqrt{2\pi}}e^{\frac{-(x-\mu)^2}{2\sigma^2}}\]

.

See http://mathworld.wolfram.com/GaussianFunction.html and http://mathworld.wolfram.com/NormalDistribution.html

Parameters

x	\(x\ (dimensionless)\) is the argument of the function.
mu	\(\mu\ (dimensionless)\) is the mean of the gaussian/normal distribution.
sigma	\(\sigma\ (dimensionless)\) is the standard deviation of the gaussian/normal distribution.

Returns

\(Gaussian(x)\ (dimensionless)\) the value of the gaussian/normal distribution at x.

See also

Gaussian() for alias.

GaussianFWHM() for full width half max of gaussian/normal distribution.

NormalDistributionFWHM() for full width half max of gaussian/normal distribution.

NormalDistributionFWHM()

template<typename T >

T EGXMath::NormalDistributionFWHM

(

const T &

sigma

)

Finds the full width half max (FWHM) of a gaussian/normal distribution.

\[GaussianFWHM(x)=2\sqrt{2 ln 2} \sigma \]

.

See http://mathworld.wolfram.com/GaussianFunction.html and http://mathworld.wolfram.com/NormalDistribution.html

Parameters

sigma

\(\sigma\ (dimensionless)\) is the standard deviation of the gaussian/normal distribution.

Returns

\(GaussianFWHM(x)\ (dimensionless)\) the full width half max of gaussian/normalDistribution.

See also

Gaussian() for gaussian/normal distribution.

NormalDistribution() for gaussian/normal distribution.

GaussianFWHM() for alias.