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In the comments of this questionthis question, it was pointed out that, when comparing two distributions, it is more natural and more general use the cumulative distribution (CDF) instead of the distribution (PDF).

The question is, why? I.e. what are the advantages (and/or disadvantages) of using the CDF instead of the PDF that make it more "more natural and general"?

In the comments of this question, it was pointed out that, when comparing two distributions, it is more natural and more general use the cumulative distribution (CDF) instead of the distribution (PDF).

The question is, why? I.e. what are the advantages (and/or disadvantages) of using the CDF instead of the PDF that make it more "more natural and general"?

In the comments of this question, it was pointed out that, when comparing two distributions, it is more natural and more general use the cumulative distribution (CDF) instead of the distribution (PDF).

The question is, why? I.e. what are the advantages (and/or disadvantages) of using the CDF instead of the PDF that make it more "more natural and general"?

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Jorge Leitao
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Why it is better to use the cumulative distribution to compute distances?

In the comments of this question, it was pointed out that, when comparing two distributions, it is more natural and more general use the cumulative distribution (CDF) instead of the distribution (PDF).

The question is, why? I.e. what are the advantages (and/or disadvantages) of using the CDF instead of the PDF that make it more "more natural and general"?