Looking for a theorem

  • Thread starter mjpam
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  • #1
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Main Question or Discussion Point

I vaguely remember a theorem that says, given a probability distribution P, there exists a transform T from P to the uniform (I think discrete or continuous) distribution.

Is this true?

Can anyone provide me with an online citation?
 

Answers and Replies

  • #4
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The uniform distribution can be transformed to any other distribution via the quantile function (i.e. the inverse CDF) but for the reverse the distribution must be continous (a continuous interval can be mapped to a point but not vice-versa).
 
  • #5
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Would it be true to say thatm given a discrete probability distribution, [itex]P_{D}[/itex], and the discrete uniform distribution, [itex]U_{D}[/itex] there exists transform
[itex]T : P_{D}[/itex] [itex]\to U_{D}[/itex] and its inverse [itex]T^{-1}[/itex] is well-deifned?
 

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