# Is distribution of CDF uniform [closed]

If I think CDF as a random variable, what is the distribution of CDF ? Is it uniform ?

Let $Y:\Bbb R \to \Bbb R$ and $X: \Bbb R \to \Bbb R$ where the latter is defined by $X(r)=F_Y(r)=P(Y \leq r)$ (so the range of $X$ is $[0,1]$ now). Now if I ask the question about the probability $P(X \leq c)=P(r:X(r)<c)$.

Note that Sample space is $\Bbb R$ here. Does this make sense now ?

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Please try to restate your question. As it is written, I can not make any sense of it. What do you mean by "think [of a] CDF as a random variable", for instance? –  Nicholas R. Peterson Sep 11 at 3:06
I think what Prasenjit means is if the distribution of a (random) cumulative density function is Uniform. Random cdf is $F(X)$ where X is a random variable having cdf F. In this case, $F(X)$ will always have uniform distribution over (0,1). This can be derived very easily by considering the cdf of F(X) and taking inverse approach. One quick intuition is for cdf being a probability, it always lies in (0,1); so is Uniform(0,1). Hope this makes sense. –  Sauvik De Nov 28 at 4:40

## closed as unclear what you're asking by Nicholas R. Peterson, Danny Cheuk, Amzoti, T. Bongers, dfeuerSep 11 at 4:12

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking.If this question can be reworded to fit the rules in the help center, please edit the question.

There can not be a distribution for CDF since it's randomness does not involve quantifiable numbers. CDF's are functions and there are infinitely many CDF's out there and their distribution can not be quantified.

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Wrong. Dirichlet distributions are an example that comes to mind. // Upvoter: why the upvote? –  Did 2 days ago