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I am sampling a random variable from a system so as to find the underlying distribution. To do so, I can plot either a histogram, or a kernel density estimate.

Either way, how do I indicate the confidence in the data?

Conventionally, when one performs an experiment, one uses the standard error (stddev/sqrt(N)) as such a measure, and if the desired y = f(x) lies within this error interval, one would say that the data suggests such a functional relationship.

How do I acheive the same for a Probability Distribtion Function instead?

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