Why Data Scientists love Gaussian?
Mathematical Reason: Central Limit Theorem
Central limit theorem states that when we add large number of independent random variables, irrespective of the original distribution of these variables, their normalized sum tends towards a Gaussian distribution. For example, the distribution of total distance covered in an random walk tends towards a Gaussian probability distribution.
The theorem’s implications include that large number of scientific and statistical methods that have been developed specifically for Gaussian models can also be applied to wide range of problems that may involve any other types of distributions.
The theorem can also been seen as a explanation why many natural phenomena follow Gaussian distribution.
Once a Gaussian, always a Gaussian!
Unlike many other distribution that changes their nature on transformation, a Gaussian tends to remain a Gaussian.
- Product of two Gaussian is a Gaussian
- Sum of two independent Gaussian random variables is a Gaussian
- Convolution of Gaussian with another Gaussian is a Gaussian
- Fourier transform of Gaussian is a Gaussian
Posted from my blog with SteemPress : https://selfscroll.com/why-data-scientists-love-gaussian/
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