Univariate and Bivariate Gaussian Distribution: Clear explanation with Visuals

Univariate and Bivariate Gaussian Distribution: Clear explanation with Visuals

Gaussian Distribution

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The mean mu is the center of the distribution and the width of the curve is the standard deviation denoted as sigma of the data series.

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How Gaussian Distribution Relates to ‘Mean’ and Standard Deviation

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Figure: 1

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Figure: 2

As the width of the curve is half the previous curve, the height became double. The range changed to -2 to 2 (x-axis) which is the half of the previous picture.

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Figure: 3

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Figure: 4

Parameter Estimation

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Multivariate Gaussian Distribution

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The summation symbol in this equation can be confusing! It is the determinant of sigma which is actually an n x n matrix of sigma.

Visual Representation of Multivariate Gaussian Distribution

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Figure 5

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Figure 6

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Figure 7

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Figure 8

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Figure 9

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Figure 10

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Figure 11

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Figure 12

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Figure 13

Conclusion

 

#statistics #datascience #machinelearning

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