02-ECDF and Histogram
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Difference between ECDF(Empirical Cumulative Distribution Function) and CDF:
The empirical CDF is built from an actual data set . The CDF is a theoretical construct.
Let
- The cumulative distribution function
F(x) gives theP(X≤x) . - An empirical CDF function
G(x) gives theP(X≤x) in your actual sample.
The distinction is which probability measure is used. For the ECDF, you use the probability measure implicitly defined by the frequency counts in your sample.
Simple example (coin flip):
Let
The CDF for a fair coin is given by:
If you flipped 2 heads and 1 tail, the empirical CDF would be:
The empirical CDF would reflect that
Why ECDF is useful?
- 1st step for data visualization. Usually along with Histogram;
- Help us to define the distribution of dataset;
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