Multidimensional Normal Distributions
Multivariate Gaussian
Settings
Visibility
Surface
Data Points
Contour / Ellipsoid
Histograms
Data Points
Number of Points:
20000
Point Size:
0.08
Point Opacity:
1.0
Graphics
Surface
Contour
X-Axis
Z-Axis
Grid
Surface Opacity:
0.6
Trace Opacity:
0.5
Contour Width:
2
Grid Lines:
10
Surface Detail:
150
Animation Speed:
4.0s
$$f(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2}$$
$$f(\mathbf{x}) = \frac{1}{2\pi \sqrt{\det(\mathbf{\Sigma})}} \exp\left(-\frac{1}{2}(\mathbf{x}-\mathbf{\mu})^\mathrm{T}\mathbf{\Sigma}^{-1}(\mathbf{x}-\mathbf{\mu})\right)$$
$$f(\mathbf{x}) = \frac{1}{(2\pi)^{3/2} \sqrt{\det(\mathbf{\Sigma})}} \exp\left(-\frac{1}{2}(\mathbf{x}-\mathbf{\mu})^\mathrm{T}\mathbf{\Sigma}^{-1}(\mathbf{x}-\mathbf{\mu})\right)$$
1D Normal
2D Bivariate
3D Trivariate
Convolve
μ:
0.0
σ:
1.0
Generate
σ
x
:
1.0
σ
z
:
1.0
ρ
xz
:
0.0
Cov(X,Z) = 0.00
Σ
1.00
0.00
0.00
1.00
Generate
σ
x
:
1.0
σ
y
:
1.0
σ
z
:
1.0
ρ
xy
:
0.0
ρ
xz
:
0.0
ρ
yz
:
0.0
Invalid correlation matrix. The combination of ρ values is not possible.
Σ
1.00
0.00
0.00
0.00
1.00
0.00
0.00
0.00
1.00
Generate